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Discrete Morse Theory is a combinatorial analogue of Morse Theory, introduced by Forman. It provides techniques for computing homological properties of simplicial sets/complexes.

1 vote

Presentation of the Rybnikov matroid

Since this is still open, I'll describe how to find an answer. You have a presentation of the matroid as an arrangement of hyperplanes. Now trace through the 'cryptomorphisms' described in the Wikip …
Russ Woodroofe's user avatar
1 vote

Morse matching with 0-cells and (n-1)-cells

In this answer, I want to 1) give a shorter approach than the above (avoiding gradient paths) to see that $\Delta P$ is homotopy equivalent to a disjoint union of bouquet of spheres plus isolated vert …
Russ Woodroofe's user avatar