0
votes
2answers
47 views

Topological dimension and derham cohomological dimension

If G is a compact complex manifold then does the topological dimension bound the deRham cohomological dimension below? By derham cohomological dimension, I mean the largest extended natrual number ...
0
votes
1answer
27 views

Is it possible to compute homology groups of a space given the Pontryagin ring?

Or similarly, given the cohomology ring of a space, is it possible to compute its cohomology groups? I'm mainly interested in integer and mod 2 homology and cohomology.
1
vote
0answers
58 views

Continuous homomorphisms

I was reading JS Milne's book on Arithmetic duality theorems and he states on page 105 that for a finitely generated torsion-free G-module (G is actually a galois group) M we have ...
5
votes
0answers
183 views

Computing the hypercohomology of a complex of acyclic sheaves

Let $K^{\bullet}$ be a cochain complex of sheaves of finite-dimensional vector spaces, I wanted to compute $\mathbb{H}^{\bullet}(X,K^{\bullet})$ = the hypercohomology of the complex $K^{\bullet}$, the ...
2
votes
1answer
173 views

Flabby sheaves and comparison of topologies

Let $A^p$ be a group of sheaves on a topological space $X$, let $F$ be the global sections functor $F(A^p) = A^p(X)$. I have to compute the cohomology of the complex $0\rightarrow A^1(X) \rightarrow ...
4
votes
1answer
182 views

injective map in cohomology theory

I have the following question, which I dont really know if its true: Let $g : X \rightarrow Y$ be a continous map between two closed, oriented $n-$dimensional manifolds such that $g^{*} : H^{n}(Y, ...
4
votes
1answer
430 views

Confused about Hypercohomology terminology and meaning

check this: Given a sheaf complex $F^\bullet$, let's say I want to compute the hypercohomology of this complex, if we consider the bicomplex of sheaves $C^\bullet(F^\bullet) = (C^p(F^q))\quad ...
4
votes
1answer
162 views

Flabby sheaves and exact sequences of sheaves - Question about proof

I was going through this proof from Rotman's 'Introduction to homological algebra' (Pages 381-382) and I just can't seem to make sense of it, am not super well-versed in this so I don't know if it's ...
3
votes
1answer
181 views

Question about proof that Flabby sheaves are acyclic

Can anybody help me understand this proof? In Rotman's 'An introduction to homological algebra' in Proposition 6.75 (iii). Flabby sheaves $\mathcal{L}$ are acyclic (Page 381), in the proof it says ...
1
vote
1answer
100 views

Is the presheaf of continuous functions on a topological space a “complete presheaf”?

Is the presheaf of continuous functions $f:A\rightarrow B$ from a topological space $A$ to another topological space $B$ a "complete presheaf"? Can't find this, anyone have a reference?
3
votes
2answers
264 views

Is the sheaf of locally constant functions flasque?

Quick question, is the sheaf of locally constant functions flasque?