The h Bar

Q: Does any non-Hausdorff manifold admit a metric tensor of signature $(p,q)$?

0

Hicks in his book, "Notes on differential geometry", works with manifolds by specifically stating that they are not required to be Hausdorff unless otherwise stated. He then goes on to define the usual manifold structures, vector fields, connections, metric tensors, etc. In chapter 6, he defines...

plz help

Anonymous

@Sumant Assam

Anonymous

2:03 PM

@0celouvsky Another JEE'r Indian :P You're screwed...the next batch is coming!

@Slereah I have the papers that talk about what I'm working on this summer

do you want to check them out?

Sure

do I have your email?

I have too many pdfs open

I should close a few

Dunno

it's slereah@yahoo.fr

lol yahoo

2:08 PM

Same email since 2001 baby

I wasn't even alive then

Ahah

check your email

Wait you were

just

a little baby

I wonder up until what point in a GR book you could drop the assumption of Hausdorfness

probably when you start talking about curves

unless you're O'neill and do the partition of unity in the first chapter

@blue jesus no

2:11 PM

drop the assumption?

spacetimes are hausdorff dammit

says u

Have you seen a spacetime in the sky

Anonymous

@BalarkaSen Prepare to do the march with Ocelouvsky :-D Naked is preferable.

i have nothing against jee

also, naked lunch, not naked march

Anonymous

2:13 PM

@BalarkaSen You told me something else in the Maths chat room :P

@Slereah what book is that?

when i say i have nothing against jee, i meant i have nothing against jee in this room

Anonymous

@BalarkaSen Oh, that's clever ;-) You hardly visit this room. I like that attitude =P

Anonymous

But don't worry. The JEE squad will soon attack the maths chat room too, in the near future =P

@ACuriousMind Hawking and Israel

2:15 PM

Why don't JEE people go to their own room

Why do you enjoy torturing us

nah. people have tried before; the only hot topic in the math chat is geometric topology

Anonymous

@0celouvsky See, I'm the nice one. I've stopped discussing JEE questions here. Not everyone is as nice as me ;)

Anonymous

@BalarkaSen That's the calm before the storm :D

@Slereah Heh

Penrose has a brief aside about non-Hausdorff manifolds

Fairly brief though

overall I think Geroch was the first guy to seriously propose them

2:18 PM

why do you want to do non-hausdorff spacetime

Before that non-Hausdorff manifolds were like

what have you been doing to your life man

"Oops I took the wrong quotient and my manifold isn't Hausdorff"

@BalarkaSen it has been proposed by some as a model for QM stuff

basically a geometric version of Everrett

allthough from the papers you wouldn't guess it

None of them even attempt to do a single particle

I don't think it's a very good model for that

mostly they just do topology

the popular model is that the spacetime would split at points along the light cone of that point

@0celouvsky got the mail

"To all the women I have loved"

Slow down, Casanova

"Don’t try to be a good man, just be a man.
-Zefram Cochrane"

Good quote, though

Haha

That dedication is pretty goofy

quite

2:27 PM

Agh, my brain. Apparently one can glue two solid tori into a 3-sphere

How

Doesn't gluing preserve genus?

Oh wait, nevermind

@ACuriousMind how?

Wait, three sphere? Wtf

I saw this in knot theory a while ago

It made sense at the time!

Glue them by the map $T^2 \to T^2$ sending meridian to longitude.

I don't know how that's supposed to explain anything

It...does make a kind of sense. You have two solid tori $D^2\times S^1$ and you glue each $\partial D^2$ to the $S^1$ factor of the other. That gives something you can't draw in $\mathbb{R}^3$, but it's fibered over $S^2$ with fiber $S^1$ so I can accept it's $S^3$

2:32 PM

@ACuriousMind that's what Elven lord did

Here's a proof. $S^3 = \partial(D^4) = \partial(D^2 \times D^2) = \partial D^2 \times D^2 \cup D^2 \times \partial D^2$

I'm not sure how to see it is the $S^3$, though

But that doesn't make the attaching map explicit unless you do it more carefully.

@ACuriousMind I think he removed a point and showed the gluing is R^3, then argued adding back the point gives the compactification

Wait, how do we get $D^2 \times D^2$ from $D^4$

2:34 PM

@Slereah Note that all the balls are topologically the same as cubes, and that you can simply build higher-dimensional cubes from lower-dimensional ones in that fashion

They are homeomorphic. Think about $D^n$ as $[0, 1]^n$

I suppose!

ACM beat me to it.

Also I didn't know that the Leibniz rule applied to boundaries

It does! That's why you use $\partial$ to denote boundaries!

Well, partially at least.

Unintentional pun too

2:36 PM

When you have an exam the next day

I was about to ask whether the $\partial$ly was intentional

and your lab mate forgets to write the lab report

so you gotta do it

but you can't even integrate

:)

Hello darkness my old friend

The integral would be the interior, I suppose

Though that only works for immersed surfaces, I suppose

What are you talking about

Well there isn't really an inverse operation to the boundary of a manifold

2:41 PM

I don't know what the correct notion of integral is. I'd look what the correct Kronecker product in bordism theory is.

oh yeah i guess it could be the cobordism

integrate those circles into pants

Bort License Plates

the greatest Simpson joke of all time

Please don't post vile things

Oh right, @0celouvsky wasn't born when the Simpsons were good

Like, literally

@Slereah How did you go from cobordisms to Bort?

I just have that joke stuck in my head

Although they do sound similar

Co-bort-ism

2:47 PM

@ACuriousMind I don't think the simpsons are family

friendly

@Slereah Is that a Siamese twin where both are named Bort?

When @0celouvsky was 7, the Simpsons were on season 16

Tough

@ACuriousMind -.-

🤦🏿‍♂️

ヽ(￣д￣;)ノ=3=3=3

What the hell is that?

Wtf did you post

2:49 PM

That's what you posted!

Apparently, that's what the "man facepalming" Emoji renders as for me

The wonders of unicode

gyazo.com/5107381714e1c15d4195cc5405e76058

It renders as nothing to me

@0celouvsky I used to watch them with my family all the time

I guess I don't have emoji font

@BernardoMeurer you probably need the newest iOS

2:52 PM

Hm?

I'm on my computer

@ACuriousMind what the hell. They're about sex and drugs and degeneracy!

🤠

Homer is a fat slob who represents everything wrong with the west

Bart should be shot

aka the average american

@0celouvsky That's...kinda the point :P

2:53 PM

The girl kid should too for being a smart ass

@ACuriousMind you're cherishing degeneracy. What the hell

Another obvious example that @0celouvsky has never seen early simpson episodes

@0celouvsky I don't really recall them being particularly about sex or drugs, except in certain episodes

@Slereah says the person who's never been to America

@ACuriousMind they're yellow

Also, you do realize the show is satire, right?

I've been to America

2:54 PM

The whole show is about being on so many drugs that the people become yellow

Drugs don't turn you yellow

You're thinking of hepatitis

@ACuriousMind that stirred some unpleasant Dead Ringers memories

@BalarkaSen I'll beat you up

"Oh, the walls are melting again"

go see a psychiatrist

or be a cenobite for that matter

2:56 PM

@BernardoMeurer Hmmm? Why would you say that?

@ACuriousMind He called my gender dumb yesterday

@ACuriousMind no

I don't know what it is

It's like that Kardashian documentary

@Bernardo If you become a Cenobite I would definitely stop calling that

I am not becoming a cenobite

I am a non-Hausdorff manifold

(Explanation for kids: Cenobites are extradimensional sexually ambivalent sadomasochistic maniac demons. They're also pretty cool.)

2:58 PM

What the HELL

I'm...not sure I'd call that an "explanation"

I'm not a masochist

@BalarkaSen you're just a kid why do you know about those things

I am a sadist though

@ACuriousMind That's the best Clive Barker gives you

2:59 PM

Am I the only one who strives for Christian goodness and wholesomeness in my life?

Yes.

I'm more of a Moloch fellow

that's where it's at

@0celouvsky they used to sell cenobite toy models to 8 year olds

when the movie got out in the 90's

They did that for everything, really

The intergalactic demons are SO EVIL

They are poisoning our children

There were alien toys, predator toys, robocop toys

Robocop was pretty brutal a movie

3:03 PM

it's pretty good tho

RoboCop Can't Stop Throwing People Through Windows

Also a lot of people get thrown through glass

the robocob dude, peter weller, also acts in naked lunch

hence my favorite actor

Have you seen Robocop 2

It is great

Robocop 2's title isn't just to indicate that it is a sequel

Ya I have

The movie is literaly about robocop 2

3:04 PM

It's curious

Kids nowadays genocide entire races in their video games, but are upset over some wars in the middle east

Well, u know

The issue of reality and all

fantastique and reality and etc

@Slereah what happens 10,000 miles away isn't any more or less real than a video game

Damn you and your local realism

reality is only real in sufficiently small balls

3:07 PM

@Slereah heh

it's a good argument tho

Where "good" means "completely bonkers" :P

How could you tell that some war in syria is real

exactly right

By going there

hence you need locality

well?

no argument?

3:09 PM

smbc-comics.com/comic/moral-relativity

Is this also a good argument

no

@0celouvsky I'm not in the mood to take your bait :P

they're forgetting the luminoferous ether

I wonder if there's an ether version of GR

After all the Lorentz ether theory is the same as SR

ok that's messed up

3:11 PM

I'm guessing ether GR would have to be Pauli-Fierz GR

@Slereah I was just about to propose that

after a loop we come back to physics, and time for me to duck out

This second paper my prof sent me has a shitload of typos

who the hell proofread this

pretty embarrassing

idk how to tell him

missing ", missing spaces

on every page

There it is

The holy grail

Is it

almost

it's for closed manifolds

for boundaries, who knows

It's funny. PDE on closed manifolds is quite easy actually

It's boundary conditions that make everything hard

3:22 PM

If it's so easy try solving a nonlinear hyperbolic PDE on the torus

@JaimeGallego What cruise trip?

Apr 11 at 20:52, by Jaime Gallego

Some of my friends are going on a cruise next week

Ah

Ah yes

The ones that made the mistake of going to Slovakia

They have money for a cruise?

I ain't shelling out 1200 bucks for that

It is supposed to be a school trip

3:26 PM

1200€ for a cruise with kids?

Why don't you tie me up to a rock and put me to swim

What kids have 1200???

@BernardoMeurer Tie you to a rock and throw you into the sea? Have you been going out with a mafioso's girlfriend again?

@JohnRennie Sadly no

Honestly that was better than the stuff going on currently

@0celouvsky Their parents do. They believe it will be an educational experience because they'll be two hours in Pompeii

1200 for two hours

3:28 PM

@JaimeGallego I believe there are some educational wall paintings there ...

Scratch that. People flag for prostitute jokes.

Date women whose boyfriends can, and will, try to kill you. That's my advice for the day folks

Ah, and Malta. But you know what kind of destination is that.

@ACuriousMind does dim_c mean anything to you?

Context of Hilbert spaces

Small c

@0celouvsky It's a variable declarator in VB.NET

3:30 PM

Not complex numbers C

What a shitty language

Wait

Does Steenrod even assume manifolds to be Hausdorff?

"We shall restrict attention to manifolds which are separable, metric and connected"

I suppose he does!

Man there's almost nothing on non-hausdorff manifolds

There's like 3 good sources, and they don't amount to much

Why exactly do you care?

Well there are some causality-related theorems with respect to non-Hausdorff spacetimes

hindawi.com/journals/ijmms/2009/891785/abs

let's investigate this paper

All topology

Where are the differential geometry papers on non-Hausdorff manifolds

@0celouvsky He's studying my sexual behavior

3:47 PM

Do the foliation sheaf manifold things have bundle structures on them?

I don't know what you're talking about

Hi, everybody.

@BernardoMeurer do you still need calculus halp?

Wtf he asked you before me?

@0celouvsky Uh, yeah. Are you surprised by this?

Foliation of manifolds are one of the rare fields where people commonly use non-hausdorff manifolds

3:51 PM

Everything is measure theory to you.

Do people define common bundle structures on them?

It is not

Tangent bundles and such

@DanielSank Later today

@0celouvsky Should I flag that?

What do you think?

3:51 PM

Go for it

I don't care

Hmmm

@0celouvsky Be Nice.

@0celouvsky y u jealous? I can explain stuff pretty well. Ask @heather.

I don't know why but non-hausdorff manifold papers are always about random boring stuff

Homogeneity and whatnot

Papers about homogeneity seem to be all alike.

3:58 PM

heyooo

@rob Do you just watch the chat and wait for a chance to make a pun? :D

@ACuriousMind I live my life waiting for chances to make puns.

Fair enough

how does Steenrod prove the existence of a Riemannian metric, anyway

Let's check

Once I sent a list of a dozen puns off to some magazine for a contest. At the last minute I removed the two silliest ones from the list. I thought for sure they were good enough to win, but unfortunately no pun in ten did.

4:01 PM

he proves it by the use of other theorems I don't know

;w;

@rob old one

@Slereah Guilty.

4:13 PM

I guess worst case scenario

I can just not care about the structures on the manifold itself and just use the ones on the Hausdorff submanifolds

Hitler Finds Out He was Not Accepted into Hogwarts

4:41 PM

@ACuriousMind how about Hitler Gets Angry videos?

Those are fine, I guess

(Although I don't find most of them funny :P)

A Hitler tampoco le gusta la bachata...

I hadn't seen that Der Untergang trailer, though, it's fantastic

@ACuriousMind I guess it's harder if the words actually make sense when you hear them

I really like this one, though

though non-Spanish speakers will struggle with it I guess

@AccidentalFourierTransform and @DanielSank might enjoy it

@EmilioPisanty Could be

I really liked the meta-video where Bruno Ganz was angry about Hitler gets angry videos.

@ACuriousMind I think these started after I had learned most of my German

it wasn't enough to make the dialogue out directly

but I did at some point look it up, and I can follow it now

and they definitely became noticeably harder to enjoy

@BalarkaSen that one is good too

5:00 PM

@EmilioPisanty I'll watch this when I get to a desktop

Have you seen the Wolfenstein one?

@DanielSank nope

what's wolfenstein

the hell is a kizomba?

"As I'm sure you know, the category of smooth (topological?) manifolds is one of those categories where the objects are very nice but the category itself is terrible. I cannot describe the number of times I've heard the algebraic geometers curse the smooth category."

nooo

not categories :(

Hitler Reacts to Wolfenstein 3D

:36861931 I imagine he means this

Wolfenstein 3D

Wolfenstein 3D is a first-person shooter video game developed by id Software and published by Apogee Software and FormGen. Originally released on May 5, 1992, for MS-DOS, it was inspired by the 1981 Muse Software video game Castle Wolfenstein. In Wolfenstein 3D, the player assumes the role of Allied spy William "B.J." Blazkowicz during World War II as he escapes from the Nazi German prison Castle Wolfenstein and carries out a series of crucial missions against the Nazis. The player traverses through each of the game's levels to find an elevator to the next level or kill a final boss, fighting Nazi...

5:04 PM

@AccidentalFourierTransform this and similar

Wolfenstein 3D was the first real time first person game I had ever seen. At the time it was astonishing. It looks, well, rather quaint now.

so... cheap electro-latino?

no wait, its from Africa

@AccidentalFourierTransform effectively, yes, though it's originally from Angola and if you do it right it's relatively different

but for all the fancy schmaltzy stuff, as always

cheap electro-afro then

How you think you look when your drunk

5:08 PM

ಠ_ಠ

cant say its inaccurate

@EmilioPisanty yep

Return to Castle Wolfenstein

5:24 PM

> Concentration made by a small thing

Mostafa

@DanielSank What sign did you eventually print on that PCB?

People here suggested those interesting hieroglyph characters

@JohnRennie I played this around 2004

Return to Castle Wolfenstein is a first-person shooter video game published by Activision and originally released on November 19, 2001 for Microsoft Windows and subsequently for PlayStation 2, Xbox, Linux and Macintosh. The game serves as both a remake and a reboot to the Wolfenstein series. This single player game was developed by Gray Matter Interactive and Nerve Software developed its multiplayer mode. id Software, the creators of Wolfenstein 3D, oversaw the development and were credited as executive producers. The multiplayer side eventually became the most popular part of the game, and was...