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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

5 votes
Accepted

How does the high-dimensional combinatorial Laplacian work?

A lot is lost in the abstract definitions of coboundary maps and cohomology (at least in the finite dimensional case, which I'm restricting to in my answer). But of course, any finite dimensional vec …
Russ Woodroofe's user avatar
1 vote

Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomolog...

You're starting from knowing that simplicial homology and singular homology are the same. Let's assume that cellular homology is a homotopy type invariant (as did some previous posters). Up to homot …
Russ Woodroofe's user avatar