1
vote
0answers
40 views
Chern Character Isomorphism for non-finite CW complexes, resp. for non-CW complexes
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 …
0
votes
1answer
61 views
Relation between $H^i_I(-)$ and $H^i_J(-)$ when $I\subset J$
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?
2
votes
0answers
87 views
Reference request: construction of Steenrod operations for an odd p
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 …
8
votes
0answers
105 views
KK-theory by abelianized correspondences of smooth stacks?
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 …
5
votes
1answer
274 views
Can group cohomology be interpreted as an obstruction to lifts?
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 …
2
votes
1answer
114 views
A group 3-cocycle, trivial on a pair of generating subgroups?
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 …
1
vote
1answer
200 views
A computation by the Shapiro Lemma
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 $ …
8
votes
1answer
263 views
“Cohomology at the infinity”: what does one call it
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 …
0
votes
1answer
191 views
Cech Cohomology of Sections of Holomorphic Bundle over Contractible Space
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 …
1
vote
0answers
87 views
Mayer-Vietoris on Fibered Products
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 …
6
votes
1answer
268 views
A formal group law over oriented bordism
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 …
1
vote
1answer
156 views
cohomology of infinite product of EM spaces
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 …
0
votes
2answers
178 views
A question on composites of pushforward and pullback
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 …
1
vote
1answer
265 views
Does the Čech cohomology always yield long exact sequences from short ones?
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 …
0
votes
3answers
308 views
Zero-cohomology of birational varieties
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 …

