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awarded  Enlightened
2d
awarded  Nice Answer
May
1
awarded  Notable Question
Apr
30
answered Cohomology ring of a fiberwise join
Apr
29
comment Table of (integral) cohomology groups of K(Z,n)
@SeanTilson: Thanks! And yes, I think there's only one paper with that title!
Apr
27
comment Table of (integral) cohomology groups of K(Z,n)
@BenjaminAntieau: Ha ha, almost! We were working out the first few stages of the Postnikov tower of $MO(2)$, in order to study realization of codimension 2 cohomology classes by embeddings.
Apr
27
answered Table of (integral) cohomology groups of K(Z,n)
Apr
23
comment The Thom space of a Whitney sum of vector bundles
I'm not sure I know what you mean by "the pasting lemma". I assume you mean the following: in a diagram consisting of two squares side by side sharing a common arrow, if any two of the `squares' are homotopy pushouts, then so is the third. Please let me know if its something else!
Apr
22
comment The Thom space of a Whitney sum of vector bundles
@Alex: You are right, this does appear to be an easier way to see it, thanks.
Apr
22
comment The Thom space of a Whitney sum of vector bundles
(This is the kind of proof I was trying to come up with, and failing.)
Apr
22
comment The Thom space of a Whitney sum of vector bundles
Thanks, this is great! I think I've convinced my self that the cofibre of $\mathbb{S}_\xi \times_X \mathbb{S}_\eta \to \mathbb{S}_{\xi\oplus\eta}$ is $T(\eta|_{S\xi})\vee T(\xi|_{S\eta})$. Now I just have to convince myself that the pushout of $\mathbb{S}_{\xi\oplus\eta}\to D\eta$ and $\mathbb{S}_{\xi\oplus\eta}\to T(\xi|_{S\eta})$ is $T(\xi|_{D\eta})$, and I'll have fully understood your argument.
Apr
21
asked The Thom space of a Whitney sum of vector bundles
Apr
19
comment How to calculate the fundamental group of general configuration space
These are called braid groups of manifolds. Key to calculations are the so-called Fadell-Neuwirth fibrations. You could probably find an answer for the torus by searching using these terms.
Apr
11
awarded  Enlightened
Apr
11
comment H-space structures on non-sphere suspensions?
Yes, I think $Y$ is actually the sphere $S^3$ rationalized. In fact, the rationalization of any odd sphere is an example of a suspension which is also an H-space (as per Qiaochu's comment).
Apr
10
awarded  Nice Answer
Apr
10
answered H-space structures on non-sphere suspensions?
Apr
6
comment How many linear independent vector fields can be constructed on a general manifold with $\chi(M)=0$?
This is called the span of the manifold $M$, and is well studied since the 1960s.
Apr
4
accepted Are there examples of non-orientable manifolds in nature?
Mar
31
awarded  differential-topology