The h Bar

ACuriousMind

3:00 PM

@0celo7 what?

@0celo7 I might find it interesting if I didn't have the suspicion you're making that up :P

Balarka Sen

@0celo7 I do not see how that's particular to Lefschetz fixed points tho.

dmckee

@0celo7 Symbol. A Generic element. I could have used the element of surprise: $\mathrm{Ah}$

0celo7

@ACuriousMind If you have a map $f$ with one fixed point, you can homotope it to a map that has (possibly many) Lefschetz fixed points

and, independent of the homotopy, the Lefschetz number remains the same

Balarka Sen

I can, like, take a smooth map $f$ of equidimensional manifolds, and take a value $x$, pullback by $f$. Pick $y \in f^{-1}(x)$.

Perturb $f$ to make it transverse to $x$. Then $y$ spits into bunch o' regular points.

Also, the sum of orientation no's is independent of how I perturb

bolbteppa

@ACuriousMind My point was that for you to have a serious issue as to the validity of my question on qualitatively predicting why $a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$ should be the answer you get for the free scalar KG field before doing any calculations, where I said I could calculate it 3 different ways, buttressed by the fact people are also voting to close a fantastic question in stage 3,

indicates a pattern of stage 2 mentality, and it should be troubling, and I want to know how you justify ignoring such a question in a way that doesn't admit being outside of stage 3

0celo7

3:03 PM

@BalarkaSen $f^{-1}(x)$ might be some fucked up shape though

if $f$ does not have $y$ as a regular value, who knows what $f^{-1}(x)$ is

Balarka Sen

Um, sure, so can be the fixed point set of an endomorphism of a smooth manifold.

ACuriousMind

@bolbteppa I'm not troubled at all that you think I have a "stage 2 mentality".

bolbteppa

@ACuriousMind If a good question is not on-topic here then the site is stage 2 level, not good enough for experts, is that really what this site is supposed to be and why lots of them left or rarely post like they used to?

Balarka Sen

@0celo7 y is just an element of f^{-1}(x)

John Rennie

@bolbteppa: ACM does not have to justify ignoring your question. That's his choice. You are not paying him to answer your question.

Balarka Sen

3:04 PM

A point out of there.

0celo7

@BalarkaSen oh, well we're talking about isolated fixed points here

ACuriousMind

@JohnRennie I'm not ignoring it, I voted to close it as unclear. That's why he's so salty.

bolbteppa

@JohnRennie obviously, but that doesn't mean I can't ask him directly

Balarka Sen

I can assume every point of $f^{-1}(x)$ is isolated too :D

John Rennie

@bolbteppa your persistence on this matter is already well beyond what many of us would consider polite.

FWIW I would answer your question if I could, but I can't.

0celo7

3:08 PM

@BalarkaSen so you think that any preimage point is just a combination of regular points of some homotoped map?

user116211

Well, sooner or later we have to think about who would be our next AMA guest after @yuggib.

bolbteppa

@JohnRennie I have mainly responded to statements directed at me, that is an absolutely amazing statement to make towards me given that, you don't consider it polite because I am calling out an issue that is uncomfortable, but I find it extremely rude to close and block good questions on this site because of some ridiculous reasoning

Balarka Sen

Yes.

0celo7

perhaps

user116211

What do you say @JohnRennie, would you like to be the next guest?

0celo7

3:08 PM

but GP think this is more interesting and deserving of recognition :P

Balarka Sen

My intuition comes from branched covers though.

@0celo7 Which is weirding me out, but ok.

0celo7

the heck

@BalarkaSen I think they're trying to find an algorithm for calculating $L(f)$ for general maps

it's easy if $f$ is Lefschetz, but in general $I(\Delta,\Gamma(f))$ might be terrible

John Rennie

@MAFIA36790 I've been asked before, but honestly I don't have anything interesting to talk about. The only thing I was even remotely expert in was colloid science, and I stopped doing that 19 years ago so I've forgotten most of it.

bolbteppa

@ACuriousMind I did not think you had a stage 2 mentality, you have great answers sometimes, I am asking about your comment on my question and where your thinking comes from on it

0celo7

so we homotopy $f$ a bit to make it Lefschetz, count the "charges" on the "scattered fixed points", then add them up to get $L(f)$

@ACuriousMind How can you not find this super interesting?

user116211

3:11 PM

@JohnRennie okayish.

0celo7

or...maybe that's not what we're doing

now they're talking about something I know as the Gauss map

Balarka Sen

Have fun.

0celo7

@BalarkaSen I'm almost done with what I want to read GP for...

on to Milnor next

bolbteppa

@ACuriousMind I then had to point out your responses thus far exclude all those amazing MO expert answers, and that it should be troubling, I can easily find questions on this site where Lubos or Ron will give some amazing insight to a question like those

John Rennie

@MAFIA36790 Colloid science is absolutely fascinating, and underlies enormous parts of everyday life. It's a great area to work in. But I just don't see it working as an AMA.

Balarka Sen

3:13 PM

G'luck

0celo7

@BalarkaSen do you know any Morse theory

Balarka Sen

Only an infinitisimal amount.

So, no, not really.

0celo7

just like you don't know any topology?

ACuriousMind

@0celo7 Well...wouldn't that analogy work for any case where there is some invariant that can be computed from a variable number of points?

Balarka Sen

No, no. I genuinely don't know this :P

John Rennie

3:14 PM

@bolbteppa for Heaven's sake give it a rest

Balarka Sen

I know what's in G&P, and I know what it does. That's about it.

ACuriousMind

I.e., I'm not sure this actually tells me something about Lefschetz fixed points in particular.

bolbteppa

@JohnRennie What's your problem with me discussing a comment he made on my question that I posted on the website last night?

0celo7

@BalarkaSen Oh, damn

user116211

Well lemme see if I can contact Valter Moretti; he would be a very competent guest. Lemme see how to contact him. May be he would be busy but why not try ;)

0celo7

3:15 PM

Luckily @ACuriousMind read Milnor and is an expert

Balarka Sen

Great, we won't see you in the math chat anymore then.

ACuriousMind

@0celo7 Ahahahahahaha...I hope that's a joke ;P

John Rennie

@bolbteppa my problem is you going on and on about it when no-one but you is interested

0celo7

@BalarkaSen :(

what did I do

user116211

@Balarka, would you like to be a potential future AMA guest?

Balarka Sen

3:17 PM

Nah, I'm fine

I should get some work done before it's too late. I want to read/watch a movie today.

See y'all.

0celo7

@ACuriousMind No, you're a super genius

I'm sure you can figure it out if you don't know it immediately

@ACuriousMind You can certainly help with algebraic topology I assume

ACuriousMind

@0celo7 Great, so you being mad at me for not actually knowing something because you think I'm just not telling you will become a regular occurence :P

@0celo7 Probably more than with Morse theory proper, at least

0celo7

@ACuriousMind you read the book!??!

bolbteppa

@JohnRennie I literally just responded to a comment directed at me, all referring back to a comment he first made on a question I posted on this site, I didn't start this, don't direct your problems through passive-aggressive comments at me please

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