Mark Grant
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 2d 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