Geometry & Topology: Dank Ass Ganja

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Balarka Sen

12:08

room topic changed to Geometry & Topology: Discussion in informal spirit [algebraic-topology] [differential-geometry] [differential-topology] [homological-algebra] [homotopy-theory]

I made the goal of the room broader than just algebraic topology - which is ok to me since many of the discussions have not been just about algebraic topology. Hopefully that would keep it more active than it is usually.

2 hours later…

Riccardo

14:26

Hi all, I'm looking for a quick reference to the computations of H^*(BSpin, Z/2) or H_*(BSpin, Z/2), where BSpin can be seen as the colimit of BSpin(k) for all k

Balarka Sen

15:22

@Riccardo I don't know a reference but I believe you can just do a Serre spectral sequence argument on Spin --> ESpin --> BSpin (the middle space is contractible). It should be a polynomial algebra on Z/2.

I take that back. I don't know how to compute H^*(Spin)

Sorry.

Heyo @Alessandro

Alessandro Codenotti

Hi @Balarka I was just following your link from the usual chatroom

Balarka Sen

I figured

Alessandro Codenotti

I didn't know there was a topology room

Balarka Sen

This used to be an algebraic topology room. We're trying to make an attempt at reviving this place

Alessandro Codenotti

So... Am I missing something or every ring (with unity) is a topological ring with both the discrete and the trivial topology?

Balarka Sen

15:33

It's true for the trivial topology; why's it true for the discrete topology?

Alessandro Codenotti

Because every function is continuous between discrete spaces

Balarka Sen

Oh right, product topology on R x R is discrete if R is discrete.

So yeah.

Alessandro Codenotti

Hm, ok, so this answer my question from yesterday regarding the coarsest topology that makes addition and multiplication continuous as functions $\Bbb R^2\to\Bbb R$

I suspect the euclidean is the coarsest topology with which $\Bbb R$ is a topological field though

Balarka Sen

The inversion is still a map R-{0} --> R; so doesn't trivial topology on R give me that?

Alessandro Codenotti

Yes but I'm looking at the coarsest one

I think that's the word in English? The smallest one when partially ordered by inclusion (assuming it exists actually)

Balarka Sen

15:41

Yeah I am confusing coarse vs fine.

Interesting; I don't know

6 hours later…

Alessandro Codenotti

22:08

@BalarkaSen Wait actually somehow I was sure you wrote discrete instead of trivial there

so that should actually work, $f^{-1}((0,+\infty))=(0,+\infty)$ where $f:\Bbb R\setminus\{0\}\to\Bbb R\setminus\{0\}$ sends $x\mapsto 1/x$ and the same works for $(-\infty,0)$

sorry I didn't notice that earlier... that's kinda boring though, maybe I should look at the coarsest after the trivial, if there is one?

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