6
votes
3answers
676 views

Applications for intersection (co)homology and for the Decomposition Theorem for students?

Which applications of intersection (co)homology and of the (Topological) Decomposition Theorem have most chances to be understood by students?
16
votes
1answer
476 views

Is there a notion of a chain complex with corners?

Roughly speaking, algebraic topology works by reducing questions about topological objects such as manifolds and cell to questions about chain complexes. On the topological side, although in the PL ...
2
votes
2answers
522 views

Non-vanishing of cup product in cohomology

Let $X$ be a smooth projective variety over $\mathbb{C}$, and let $\alpha \in H^{2k}(X)$ be an algebraic cohomology class. Let us fix an $l$ such that $H^l(X) \neq 0$ and $H^{l+2k}(X) \neq 0$. The ...
3
votes
2answers
401 views

Stratified Pseudomanifold

Hi there, I have a, I guess, simple question. In the definition of an n-dimensional stratified pseudomanifold one demands the following filtration $X=X_n \supset X_{n-1}=X_{n-2} \supset X_{n-3}\supset ...
2
votes
0answers
246 views

The signature of a mapping torus

Consider a manifold $M$ of dimension $4k + 2$, $k$ an integer. Pick a diffeomorphism $\phi$ of $M$ and construct the mapping torus $T$ of $\phi$. Suppose that there is a $4k+4$ dimensional manifold ...