I'm not even sure what it is for $n\ne 3$.

The statement of the conjecture, that is

No, there is no smooth h-cobordism theorem for n = 4.

@0celo7 Hmm? What conjecture?

Poincare.

@BalarkaSen I did not say there was.

Homotopy equivalent to $S^n$ implies homeomorphic/diffeomorphic/PLeomorphic to $S^n$.

My advisor also suggested "Introduction to the $h$-Principle"

@0celo7 You wrote n>=4 at first. But I see you edited.

Although that might require too much PDE

good lord

this seems to be some high-power stuff

Hello @DanielSank .

@vzn I'm happy to be a guest in 4 weeks. As for updating the meta post, note that you can edit it!

h-cobordism is cool beans; I wish I knew more about it.

@DavidZ And for those time slots we are most grateful.

@DanielSank >:(

@ACuriousMind $h$-principle involves sheaves. I hate my life.

@DanielSank cool :) hey are you back from japan yet?

???

@BalarkaSen where do I learn about jets

@0celo7 Etiquio Young "Vector and Tensor Analysis" does the exact same thing for another reference, I think the problem is you just need to understand why old-style tensor analysis (also called physicists tensor analysis, index gymnastics etc...) is the same as modern linear-algebra-based tensor analysis just a bit uglier at times (but actually nicer at others)

Ask Ted. I don't know anything about those.

To actually sound like John, I'll just say Einstein used the old-style stuff :p

@DanielSank "edit" is dimmed out/ disabled for me on meta for that post & others, think its because its not community wiki, there seem to be stricter edit reqs/ restrictions in meta

Jets are when you analyze PDE's on manifolds

Or even Taylor expansions

Higher derivatives basically

Through truncated polynomials

I do not think that those last 4 messages successfully explain or motivate what jets are.

@BalarkaSen He asked where do I learn about them, I mentioned some places they come up :\

@0celo7: At least I'm rather certain that you have seen a jet in the sky :P

I notice this happening a lot

@bolbteppa OK. You started the first message in a way as if you were trying to explain the concept.

@bolbteppa I was thinking the exact same thing.

"Jets are" etc.

I would not take the risk since you called me crazy last time I tried to explains something to you

@ACuriousMind What is the cohomology of a group???

That's not even a Lie group???

What the hell is a cohomology

@0celo7 Ah, that's a bit tricky.

@0celo7 If G is a group, there is a space associated to it called the K(G, 1)

That has fundamental group isom to G, and all the higher homotopy groups 0 (yes, such a space is unique, upto homotopy equivalence)

Cohomology of that space is called the cohomology of G.

^the space is called the classifying space, and also written BG.

"the cohomology groups of a finite cyclic group are non-trivial in arbitrarily high dimensions"

???

He promised me Milnor requires a minimum of algebraic topology

!!!

"Minimum" is relative.

Are you really reading Milnor's Morse theory?

I can't imagine him discussing cohomology of groups there.

@BalarkaSen Flipping through it

I have like 2 pages in GP left

Then exercises

Then on to Milnor

Maybe he's just saying that group cohomology thing while passing by.

Hmm?

@0celo7 Let me know when you have understood the Lefschetz hyperplane theorem.

@BalarkaSen where is that

@BalarkaSen it's used in a proof

He proves it somewhere in the end of the 1st chapter, IIRC.

Oh, in Milnor

Thought you meant GP.

Nah

@BalarkaSen But next summer: Bott-Tu & Giant Milnor.

I wish you luck.

This year: $h$-cobordism if I have time.

I will be happy if I can read that small book in a year.

Your reading style is a bit different than what I would prefer, but eh, each to his own.

Because I will not have much time

@BalarkaSen what would you prefer

Working through hard exercises.

I do not find that enjoyable or constructive.

sure

99% of the time exercises are "hard" because there's some trick.

By exercises, I don't really necessarily mean exercises out of some book.

I'm not good enough at math to do arbitrary exercises.

Thinking about questions, mostly. E.g., I just proved something about the homotopy type of the space of maps between equidimensional manifolds using the transversality theorem. That was fun - I didn't find it any book, just wondered about it randomly. Proving stuff, answering questions, etc is fun.

I'm not good enough at math to do that.

I think too linearly.

That's what books like the $h$-cobordism theorem are for.

Time to get #rekt by Milnor.

@BalarkaSen

With great difficulty.

@0celo7 Yikes.

Time to learn algebraic topology? :P

I think the font's quite cool.

Have you seen the h cobordism font

It's pretty terrible

Nope, not really.

@BalarkaSen Why do you keep coming to this chat

Seems fine to me.

@0celo7 I don't know, I really shouldn't.

Why not?

It's not like we discuss physics in here.

@0celo7 This is why.

What?

Also, because you are here

Oh you

I'm the only one willing to talk to you

Really, I waste much of my time chatting. Maybe I should be gone, like Mike.

Did Mike legit quit chatting?

I think so.

I understand page 1 of Milnor.

Praise be.

@BalarkaSen ??

Why

I talked to him on e-mail, so he's alive at least.

I dunno. Everyone needs a break.

@ACuriousMind You better not need a break

He's getting some constructive work done, at least.

OK, I should sleep now.

Good night.

@JohnRennie What?

@ChrisWhite Could you please provide a reference for the Newtonian Friedman thing?

@3750 I'm no longer discussing math with you.

But if you want to talk physics, go ahead.

I'm certain I helped you somewhere.

Ok, then I didn't.

What difference does it make?

@yuggib For some reason my mental image of you is that one french dude

Groeten something

Was Grothendieck insane?

@3750 Let's talk physics.