This is a question I asked at Math.SE but got no answers: http://math.stackexchange.com/q/397164/7110/ Atiyah and Hirzebruch showed in their paper "Vector bundles and homogeneous …

What is the relation between $H^i_I(-)$ and $H^i_J(-)$ (cohomological functors) when $I\subset J$ are ideals of a (local) noetherian ring?

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 …

Whith (Kasparov, bivariant) KK-theory I am left with the nagging feeling that the theory is "more fundamental", than has been made explicit, that there is a "more profound" univers …

The standard way to view the first and second group cohomologies is this: The Standard Story Let $G$ be a group, and let $M$ be a commutative group with a $G$-action. Then the fi …

I'm looking for an example of the following situation: A group $G$ generated by finite subgroups $H$ and $K$, a non-trivial 3-cocycle $\omega \in H^3(G, \mathbb{k}^\times)$ suc …

Hi: When I read the book "An introduction to Homological algebra" by Weibel, the page 206, line 9 says that "Shapiro's Lemma tell us that $H_q(S_n(X)\otimes_{Z}A)$ is zero if $ …

Suppose $X$ is a "good enough" Hausdorff topological space; we assume that $X$ is not compact. Now, for a natural number $k$ and an abelian group $G$, consider the group $\varinjli …

Is there anything that can be said in general about the Cech cohomology of the sheaf $\mathcal{F}$ of sections of a holomorphic bundle over a contractible space $X$? I know that …

Suppose $M \xrightarrow{p} X$ is a surjective submersion of smooth manifolds. Define the fibered product in this case: $$M \times_X M = \{ (m_1, m_2) \in M \times M | p(m_1) = p(m …

My question is related to the following question by Mark Grant here on math overflow: http://mathoverflow.net/questions/74770/formal-group-law-of-unoriented-cobordism There it is …

Is it true that any map from an infinite product of Eilenberg-MacLane spaces in to an Eilenberg-MacLane space factor through, upto homotopy, a finite subproduct? Even if we take wi …

Let a finite group $G$ acts on an orientable manifold $X$ freely. Denote $\pi:X\rightarrow Y=X/G$ be the quotient map. This covering map defines two maps between cohomology groups …

Does the Čech cohomology always give rise to a long exact sequences given a short exact sequence of sheaves? Clearly that cannot occur for sheaves on a paracomact (perhaps also Ha …

Let $f:X\dashrightarrow Y$ be a birational map of smooth projective varieties, i.e., there exist open subsets $U_1, \subset X$ and $U_2 \subset Y$ such that $f|_{U_1} : U_1 \righta …