-2
votes
0answers
57 views

Why Must the Degree of this Map be 0? [on hold]

Let $f:S^3 \rightarrow S^1\times S^1\times S^1$ be a continuous map. Show that it's degree must be $0$. (Just a hint would be good)
2
votes
0answers
57 views

Long Exact Sequence Cohomology with Compact Support

I found in this topic or (question) a reason for my question, but i do not understand it. As this question is quite old, I hope someone else can help me. Assume $U$ is an open subset of a topological ...
0
votes
2answers
46 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 ...
4
votes
1answer
79 views

If M is a non-orientable closed connected 3 manifold prove H1(M) is an infinite group.

This is an example from a question sheet (non-assessed) of a university class. If M is a non-orientable, closed, connected 3 manifold, prove $H_1(M;\mathbb{Z})$ is an infinite group. I know that since ...
5
votes
0answers
93 views

Cohomology of covering space

Let $B$ be a base space and $E$ be a covering space of $B$ what is the relation between $H^2(B,\mathbb{Z})$ and $H^2(E,\mathbb{Z})$.?
3
votes
2answers
264 views

Is the sheaf of locally constant functions flasque?

Quick question, is the sheaf of locally constant functions flasque?
16
votes
3answers
1k views

Motivating Cohomology

Question: Are there intuitive ways to introduce cohomology? Pretend you're talking to a high school student; how could we use pictures and easy (even trivial!) examples to illustrate cohomology? Why ...