random cohomology for quantum nerds

« first day (1476 days earlier) ← previous day next day → last day (107 days later) »

5:21 AM

The Wikipedia article Cohomology with compact support (current revision) has this post among the references: Cohomology with support and Poincare duality

Cohomology with compact support

In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. == Singular cohomology with compact support == Let X {\displaystyle X} be a topological space. Then H c ∗ ( X ; R ) := lim...

Q: Cohomology with support and Poincare duality

Say we have hypersurface $D \subset \mathbb{P}^2$. I ran into the following sequence of isomorphisms, justified only with "by Poincare duality formulated algebro-geometrically": $$ H^2(\mathbb{P}^2-D,\mathbb{Q}) \cong H^3_D(\mathbb{P}^2,\mathbb{Q}) \cong H_1(D,\mathbb{Q}) $$ I looked up cohomolog...