Dear all, I stumbled on this question due to an application in physics, but I find it hard to find useful references for it. I looked into literature on projective geometry and po …

Where in literature can one find a construction of Steenrod reduced powers (for an odd $p$) that (1) works for the singular cohomology of arbitrary topological spaces (or, more …

In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{ …

I would like to know the ring structure of $K(Q_n)$ explicitly where $Q_n \subset \mathbb{P}^{n+1}$ is the non-singular $n$-dimensional complex quadric and $K(Q_n) = K^0(Q_n)$ is …

Suppose that you have decomposed a manifold $M$ into cells (I care most, if it matters, about compact oriented smooth manifolds; but if my question can be solved in the PL category …

I have the following situation. $M$ is a combinatorial model category, or if you like a locally presentable $(\infty,1)$-category. I have a set of maps $S$ and I let $C$ be the cla …

By site of manifolds Man, I mean the category of manifolds (maybe submanifolds to obtain a small category) with continuous maps between them. A Grothendieck topology is given by op …

What is $\pi_{31}(S^2)$, the 31th homotopy group of the 2 - sphere ? This question has a physics motivation: 1) There are relations between (2nd and 3rd) Hopf fibrations and (2 …

Cobordism genera can often be refined to $E_\infty$-orientations in the sense of Ando-Blumberg-Gepner-Hopkins-Rezk: 1) the mod 2 Euler characteristic $MO\to H\mathbb{F}_2$; 2) th …

It has been asked here, whether a retract of a finitely presented group is again finitely presented, i.e. if $G$ is a finitely presented group and $H$ is a group which fits into a …

I would like to know what has been done in terms of specific calculations for the cohomology of principal bundle. For instance, it is known (see e.g. Greub, Halperin and Vanstone's …

I would guess that the following is true, and that somebody has worked it out, but I don't recall ever seeing it. Can anyone point me to any literature on it? Let $G$ be a finite …

I have encountered a certain generalization of the Lefschetz fixed point theorem as folklore, and I am hoping that someone out there knows its provenance or can otherwise refer me …

As pointed out by David White in http://mathoverflow.net/questions/73687/when-mapping-cone-is-contractible there exists an acyclic CW-complex $X$ which is not contractible but who …

In his book Quantum invariants of knots and 3-manifolds page 124, Turaev defined a TQFT $\tau$ axiomatically. For a cobordism $(M, \partial_{-}M, \partial_{+}M)$, a TQFT assignes …