Mathematics - 2016-07-28 (page 2 of 3)

@ForeverMozart Hi

you are topologist

You will have time to fix more typos in the proofing stage anyway

I am no such thing :)

How dare you.

oh so I should not panic

It just looks so bad now that I see it

oh wow you have many papers

and not in topology :)

I caught a typo in one of my papers as I reviewed the proof before uploading to arXiv. I had accidently pasted the wrong title for one of the papers in the references (I would probably not have caught it if it had not happened to be identical to the title above it)

Right, none in topology

7:51 AM

well at least mine is not in the title, it is in the introduction

I left out an "a"

This was in the title of a paper I cited (except it had the entirely wrong title as I had reused parts of the bibtex code for it and forgotten to change the title part)

like "he was good boy" instead of "he was a good boy"

@ForeverMozart That just makes you sound Russian

or possibly Japanese

yes

but I am Canadian

I am a Canadian

see it happens all the time

Anyway, you will have the opportunity to correct it (at least two such even. When responding to reviewer comments and when receiving the final proofs)

it sounds wrong with the "a"

or rather, it sounds like it lacks a noun.

7:57 AM

That is good. I hope it goes straight to the proof stage, but I am told it is rare.

Yeah, I think it is really rare for the reviewers to suggest no changes at all (I had a 3-page paper accepted within three days, and even there the reviewer had a small suggestion)

should I put it on arxiv now?

@ForeverMozart If you have submitted it then yes, definitely

oh, why?

I would even have done that a bit prior to submitting it, as it might get useful comments (though probably rare for those to come fast enough that you can implement them before submitting anyway)

My latest arXiv paper has not in fact been submitted anywhere yet, even though it has been there for a few weeks

8:02 AM

Should I ask my advisor?

or is it standard?

The answer to that question will almost always be "yes".

but it is completely standard to put everything you publish or plan to publish on the arXiv

what are the risks of not putting it there?

not really any risk. It may just not be read by as many people

Also, it is nice that people can read it already now, rather than having to wait until it gets published which may take more than a year

wow I hope it only takes 2-3 months

that would be really fast (way faster than any of my papers so far certainly)

8:05 AM

I think most mathematicians would think my paper is very simple

even getting reviews back within 2-3 months would be on the faster side of the norm

I just put together a couple of ideas

I have a 10-page elementary paper that the reviewer took a year to review (he did apologize for being slow to do it, but still..)

wow

review times and time to publication following the review vary wildly based on all sorts of factors that are impossible to control

hence why the arXiv is so nice to have

8:06 AM

I can update versions on arxiv, right?

yes

To compare, y first paper was accepted within three days, then took another approximately 18 months to get published. Whereas my recent paper in Advances took almost a year to review and accept but was then published online very shortly after and will appear in print in October (which will be about 3-4 months after the accept)

ok I will email my advisor, he will probably say yes

is it a joint paper?

no

just me

Ok. Then of course you don't really need his approval, though it is always good to talk about these things with your advisor to learn about how things are done

8:09 AM

I think the process should take 6 months maximum

which journal is this?

because otherwise advances may go beyond your paper

again, this is the reason for arXiv

I hardly ever read any new papers in the actual journals. I only find older papers there when people mention them or when I need a proper reference for them when citing them

it is Fundamenta Math., .5 impact factor

everything else I get from arXiv (I have an rss feed for group theory and representation theory)

8:11 AM

Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.

Impact factors mean fairly little for math journals, as citation counts vary so wildly between subfields. But Fundamenta looks to be very solid (ranked A on the old Australian list)

group theory was like everything is super easy for a while, and then I went to class one day and we were doing crazy things

nilpotent

if you connect 6 points with red and blue lines, you will always get a red or blue triangle

that is fun to prove

@TobiasKildetoft do you read philosophy?

@ForeverMozart As long as you make a complete graph

Not when I can avoid it

(which I usually can)

today I got Heidegger Being and Time

I read a lot of existential philosophy, but Heidegger is supposed to be very hard to understand

Albert Camus The Stranger is my favorite book

have you read that?

nope

8:19 AM

you can read it in one sitting

please do it

As I said, I prefer not to when I can avoid it. I have so many other things I would rather read

I just had a look at impact factors of some math journals out of curiosity. .5 seems right in the "decent but nothing spectacular" camp (assuming that impact factor actually has a meaning)

yes it is not like AMS or something

Well, AMS has several journals (not sure if they are all above .5 impact factor)

JAMS has like 2.5-3 or something like that

they would reject me :(

Transactions has about 1.2 (I submitted a paper there recently)

not sure about the others

8:33 AM

maybe the impact factors are less if the journal is in a specific area

like to get in JAMS you have to compete against all mathematicians

I think so, yes. Unless that area is one that tends to have long bibliographies, then probably the impact factor is larger than it would normally be for the prestige of the journal.

There are plenty of journals that do not really specialize but do not have particularly large impact factors

well I have to go to bed

hopefully when I wake up it wont be rejected :|

Heh

it is morning in Poland!

But the reviewer might be based in Australia :)

8:37 AM

oh yeah

anyway, talk to you later

(as might the editor for that matter. Not sure if you picked a specific one or if the journal picks one for you)

cya

10:16 AM

yo

any1 here/?

@ManolisLyviakis Not many at the moment I think

hey

How good is your topology?

im a bit noob

and wanted to ask soomething

it is decent, but not my specialty

algebra?

is ur specialty?

i Came across a definition on connectedness and open relatively sets.

that when i try to confirm them in a pictorial way i couldnt

$U\subset S\subset C$. We say that $U$ is relatively open in $S$ if for every $z_0 \in U$,
there is $r > 0$ such that
$$D(z_0 ;r)\cap S\subset U$$:

A set $S \subset C$ is called connected if the only relatively open and closed sets in
S are the empty set and S.

@ManolisLyviakis Only clopen subsets are empty and all?

10:21 AM

??

@ManolisLyviakis That is the same thing

The only clopen (closed and open) subsets are the empty set and the whole set

the definition says if the only relativevly open and closed sets are the trivial then it is connected

i thought of a set that is not connected say 3 open balls and tried to use the definition to prove that it is not connected that means i tried to find a closed relatively open subset of the 3-open balls that is not trivial.

So my question actually is using those 2 definitions Prove that the set of 3-open ball is not connected.

@TobiasKildetoft so?

@robjohn didnt understand what you said

@0celo7 Is that by Krek?

I remember Mike mentioning that.

am i asking something wrong?

logically wrong*

oh well :'( cant figure it out.

The problem is if i take a closed subset of the 3-open balls set

at the boundary of this closed set

i cant find r>0 such that the r-ball around the point at the boundary intersection with my initial set would be subset of that closed subset. If my initial set was $Z$ i could take r=1/2 and for a closed set i could take just the 1 element set {1} .Closed and realitively open and not trivial subset so $Z$ is not connected.

no1 can help?

10:54 AM

well.

cant find a sollution

im gonna leave it

11:24 AM

can sets be relatively open and relatively closed as subsets of a set K with a topology?

at the same time?

user 1618033

12:36 PM

Let me see if I can edit messages

(yes, it works - but with some delay though)

@BalarkaSen Kreck.

Alex

12:56 PM

Hi there. I have an applied problem, but I'm a noob at solving such problems. The best I could achieve is to reduce the problem to one-dimensional: given a
sequence of n uniformly distributed points x_i in some interval we should find the x(t) and sequence of t_i with the following restrictions: |dx/dt|<A; |d2x/dt^2|<B; x(t_i) = x_i; t_(i+1) - t_i = k_i*C, where k_i is natural number; t_n-t_1 (full time) should be as minimal as possible from all solutions. What should I do next to find the solution?

@ManolisLyviakis the same thing as you said. A space is connected if the only closed and open sets are the empty set and the whole space.

ye i got it .was a silly misunderstanding on what relatively open and closed meant. i thought it meant a closed set on C that is relatively open in another set.But it means relatively closed and relatively open in a set

@robjohn

May i ask now a sillier question? @robjohn

@ManolisLyviakis you can always ask...

I have to prove that the $f(z)=f(x+yi)=sqrt{|xy|}$ satisfy the rieman-cauchy eq at the point (0,0) but is not differentiable at (0,0). What i did was this

$\sqrt{|xy|}$ *

$|xy|=\sqrt{xy^{2}}$

so $f=\sqrt[4]{(xy)^2}$

now i split $f$ to $u$ and $v$ imaginary and real part

$u_x$=$v_y$

$u_y=-v_x$

$v=0$ because imaginery part is zero

so i have to prove that the partial derivative of $u=\sqrt[4]{(xy)^2}$ at zero is zero

Exercise: Read arxiv.org/abs/1607.07345 and find an example of the sort of object the paper is about (the author does not seem to give any)

1:10 PM

so i differentiate with respect to x and i got $u_x=\frac {xy^2}{2|xy|^{3/2}}$

at x=0 i get 0/0

:"(

how do i prove the partial derivatives satisfy the riemman eq.Proving that the function aint differentiable at zero is easy.

any1 can hellp me?

Q: How to solve this hard equation?

1:28 PM

i said if $xy=0$ f(z)=0 so partial derivative is zero :P

YeuSeChia

1:56 PM

-2

I have read this equation on a journal: $3\left(\log _3( {\sqrt {2 + x} + \sqrt {2 - x} }) \right)^2 + 2{\log _{\frac{1}{3}}}\left( {\sqrt {2 + x} + \sqrt {2 - x} } \right)\cdot {\log _3}\left( {9{x^2}} \right) + {\left( {1 - {{\log }_{\frac{1}{3}}}x} \right)^2} = 0$ I tried to solve it; but,...

logarithms

2:13 PM

seems like a numerical analysis problem

@YeuSeChia

well maybe transform the logarythm to the same basis

$log_b(x)=\frac{log_c(x)}{log_c(b)}$

2:40 PM

can a function be differentiable from $R^2$-->$R^2$ and not be analytic?

3:17 PM

@ManolisLyviakis Yes. $e^{\frac1{x^2+y^2-1}}$ for $x^2+y^2\lt1$ and $0$ for $x^2+y^2\ge1$ is $C^\infty$ but not analytic.

3:35 PM

@BalarkaSen: do you know the $9g-9$ theorem?

csss

3:54 PM

I am not familiar with Lipschitz domains. What should I think of when I hear the phrase Lipschitz domain? Is this a domain with corners? Or without corners? Or does it imply a domain with corners that are 'sharp' in that the derivative goes to infinity at the corner? Just looking for some intuition for these domains?

iwriteonbananas

4:13 PM

@archipelago Cool, I wasn't aware of that fact. Good argument though.

4:30 PM

Today is my 5 year anniversary on MSE!

another hour and a half ;-)

@robjohn: happy anniversary, I can't believe I've been longer on MSE than you

@Huy I didn't hear about MSE until about a year after it started. I was on sci.math and then came here, never looking back.

4:57 PM

@Huy Hmm, no, what does it say? I have heard of something called the 84g - 84 though.

I wonder if there's a connection.

5:13 PM

@BalarkaSen: 84g - 84 is Hurwitz, a bound for the number of automorphisms of a Riemann surface with $g \geq 2$

yup, I am aware

what's the 9g - 9 theorem?

@BalarkaSen: you're aware of the length function from Teichmüller space to $R^S$ where $S$ is the set of isotopy classes of simple closed curves, yes?

um, no. I don't really know what the Teichmuller space is

@BalarkaSen: "hyperbolic metrics up to isotopy"

what do you mean by isotopy of metrics?

5:15 PM

basically you take a hyperbolic metric and compute the length of the unique geodesic in each isotopy class

@BalarkaSen $Diff_0(S)$ acts on hyperbolic metrics by pullback

and you define Teich = HypMets/Diff0

ah

does the map make sense?

what's $R^S$?

you mean, $\Bbb R^S$?

yes, of course

all of that makes sense, yes

5:24 PM

ok, so it would already be pretty cool to show that map is injective, right?

("hyperbolic metrics up to isotopy are uniquely determined by their length function")

yeah. but one thing, why is it well-defined?

that is to say, why do you get the same length after acting by a Diff_0 element? I am not sure why the map preserves that action

@BalarkaSen: there's actually another definition for the Teichmüller space which is usually used in arguments, the one I've given allows one to "explain what it is" faster, that's why I used it, but I can quickly write down the other definition and why it's well-def

sure, write it down if you want to, otherwise forget it. I'm listening in any case.

5:44 PM

@BalarkaSen: Let $S = S_g$ with $g \geq 2$. Call a "marked hyperbolic surface" a pair $(X,f)$ such that $X = \mathbb{H}^2 /\Gamma$ is a hyperbolic surface and $f: S \to X$ an orientation-preserving homeo. Given $(X,f)$ you can pull back via $f$. Define the Teichmüller space of $S$ equivalence classes of marked hyperbolic surfaces where $(X,f) \sim (Y,h)$ if $h \circ f^{-1}$ is homotopic to an isometry $X \to Y$.

fix $(X,f)$. now given an isotopy class of an scc $\alpha$ on $S$, there is a unique simple closed geodesic on $X$ that is homotopic to $f(\alpha)$. define the function

(correct me if something's wrong or you think something needs a lot more justification, I'm also just starting to learn about Teichmüller spaces)

Ted Shifrin

Happy anniversary @robjohn. I don't even remember any more how I landed at MSE. Pedro dragged me into chat for the first time; that I remember.

Hi @Huy @Balarka

Hi @Ted.

hey @TedShifrin

@Huy Ah.

This is equivalent to the previous description because one can pull the metric on $\Bbb H^2/\Gamma$ back to $S$, yeah?

yes (that's how I understand it)

Ted Shifrin

5:47 PM

@Balarka: There was a long post I glanced at. What's the easiest example of a map $f\colon X\to Y$, $X,Y\subset\Bbb R^2$, with $f$ closed but neither open nor continuous?

@BalarkaSen: ok, now as I said it would already be pretty cool if the map $\ell: Teich(S) \to \mathbb{R}^{scc}$ was injective (I realized it's not smart to use $S$ twice)

the 9g-9 theorem says that it's actually possible to pick just 9g-9 simple closed curves in $S_g$ so that the map
$$(X,f) \mapsto (\ell_{\alpha_1}(X,f), \dots, \ell_{\alpha_{9g-9}}(X,f))$$
is injective

(sorry, the map in my message a bit earlier of course should have an index corresponding to the scc)

(I also should have switched the places of the scc and the marked hyperbolic surface i.e. $\ell_X(\alpha)$)

@TedShifrin: do you know about this stuff? I'm trying to find or figure out a proof that $\ell$ is injective before I work on the 9g-9 theorem

@TedShifrin Hmm. There should be not too hard one dimensional examples.

E.g., take a very disconnected open set $U$ of $\Bbb R$ (maybe a thickening of the cantor set?), send $\Bbb R - U$ to $\Bbb R$ by mapping each closed interval component in it homeomorphically to $[0, 1]$ and the two unbounded components to $0$ and $1$ respectively. That shouldn't be open.

Yes, it's not. Take the open set consisting of all of $\Bbb R - U$. That maps to $[0, 1]$, which is closed in $\Bbb R$.

So there you go.

@Huy ah, nice

6:03 PM

@BalarkaSen: so my original plan was to ask you if you knew anything about how to show that $\ell$ is injective, but I guess I don't have to ask. :P

obviously not

I know nothing of this

=(

What kind of things can one do with the Teichmuller space?

@BalarkaSen: since I just started looking at the chapter about Teichmüller spaces, I obviously don't know a lot yet, all I know from the introduction is that Teich(S)/MCG(S) = moduli space of Riemann surfaces homeomorphic to S and the three spaces seem to have an interesting "interplay", e.g. I think MCG acts properly discontinuously on Teich(S)

@Huy i see

6:10 PM

apparently moduli space of S is equivalently:
1) isometry classes of constant curvature metrics on S
2) conformal classes of Riemann metrics on S
3) biholomorphism classes of complex structures on S
4) isomorphism classes of smooth, complex algebraic structures on S

yes, there's a trend among people - mostly geometric group theorists - to study weird groups by looking at what kind of object it acts on

this gives interesting results very often

(and those bijections apparently rely on other very deep theorems)

@Huy nice!

(4) is quite weird

hehe

if I find out more interesting things about Teich(S), I'll report it :P

but for now I'm already enough impressed by the 9g-9 thm

sure thing

6:16 PM

Good afternoon

Krijn

Sup all?

Hi 0celo, Krijn

Where is Ted when you need him

Semiclassical

6:41 PM

hi chat

@0celo7 Out of curiosity, did you read G-P's rant on motivating the Whitney embedding theorem?

I wondered whether that can be made rigorous.

@BalarkaSen Perhaps, but it didn't stick with me. Page?

I wasn't very concerned with that section

@Semiclassical Hi.

I don't remember the page number. Essentially, if $X$ is an $n$-manifold, you first try to construct an immersion into $\Bbb R^{2n+1}$. The image self-intersects itself. Note that dim X + dim X = 2 n < 2n + 1 (dimension of the ambient Euclidean space). So if you try to make the image self-transverse by transversality theorem, then it becomes disjoint from itself, hence becomes a manifold.

Yeah, reading it right now

You have to do this with care, though, so that it remains an immersion at each stage of the homotopy.

But this was an exercise in G-P that it can be done.

6:54 PM

@BalarkaSen yes, we did it.

Mike said it isn't any easier to construct an immersion into R^{2n+1} though :(

@0celo7 Mhm

GP says that modeling a proof on this is hard...

But maybe it can be done?

I wonder where the $2k$ result is proved.

Probably just because that it talks about transversality in chapter 2 not 1. Also, self transversality is a subtle thing.

Is it in Hatcher?

@0celo7 I asked Mike; he said there's no use.

$2k$ result?

6:56 PM

$M^k$ can be embedded in $\Bbb R^{2k}$.

Nah.

It's probably in Hirsch. I'll read it later, don't care right now.

Coincidentally, I have Hirsch in my hand.

I am going to work out why and how self transversality works.

It's not, he gives a reference to the original paper.

@BalarkaSen What do you mean?

@0celo7 Transversality of an immersion with itself.

6:59 PM

What's so crazy about it?

How do you know the usual results work for those too?

It's worth sitting down and proving them.

Are you talking about self-intersection theory?

Besides, you need good immersions. An immersion with a triple point, and everything's wrong.

Stuff like $I(Z,Z)$ (or mod 2)

No.

Self-intersection theory is for a manifold with a perturbed copy of itself.

7:01 PM

@BalarkaSen Yes

I'm confused by what you're looking for then

I'm looking at an immersion. E.g., take a figure eight on a plane.

Ok

So, why are such "good" immersions open in the class of all immersions?

Hmm.

Seems like the same argument would work.

Right, that's easy.

7:32 PM

@BalarkaSen Uhh, what do you mean?

Stability of self-intersection.

No, what do you mean by "open in the class of all immersions"

An arbitrarily small deformation is also a good immersion?

Yes.

Then yeah, that's stability of transversality

I think

But you have to prove it.

7:34 PM

Hmm, how does transversality apply to self-intersection

What does the transversality equation look like

If $f : X \to Y$ is an immersion which is good aka there aren't three points which gets mapped to the same point, then for all pairs $x, y \in X$ w/ $p = f(x) = f(y)$, $df_x T_x X + df_y T_y X = T_p Y$.

Huh, Hirsch defines them a little differently by giving nicety conditions near $x$ and $y$ too - namely, that $f$ is an embedding near $x$ and $y$.

I guess I do need that.

Right, the double points must be isolated. Otherwise I am doomed.

Semiclassical

@BalarkaSen Doooomed.

What's up?

Semiclassical

7:58 PM

Not much. Reading up on the inverse scattering transform.

and trying to figure out if it actually helps for what I'm interested in