# Tag Info

Accepted

### Restriction vs. multiplication by $n$ in Tate cohomology

Let $G = \Bbb Z/4$, acting on the Gaussian integers $M = \Bbb Z[i]$ via multiplication by $i$. The transfer $M_G \to M^G$ is given by multiplication by $1 + i + (-1) + (-i) = 0$, so H^{-1}(G,M) = ...
• 48.1k

### Dual surfaces of a first cohomology class of a 3-manifold

Some things are known in the non-orientable case (in orientable 3-manifolds). Bredon and Wood work out the genus in lens spaces $L(2n,q)$ (and some other manifolds) in their paper Non-orientable ...
• 17.8k

### How to define cohomology of algebraic structures?

There is a tremendous amount of abstract formalism answering this question in various levels of generality depending on what you want to do. I'll pick one in the middle: the machinery of derived ...
• 109k
Accepted

### Formula for the Euler characteristic of a local system on $\mathbb{P}^1$

The answer to your question at the end is negative. In fact, $h^2(D, j_*F)= h^2(D, j_* F)=0$. In fact, the cohomology of a sufficiently small disc around a point in any complex variety, with ...
• 119k
$L(4,1)$ is a counterexample to your conjecture, taking $\alpha$ to be the nontrivial element of $H^1(L;\Bbb Z/2)$. Notice that this element squares to zero (the square is the same as the Bockstein, ...