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Mathematicians have long been interested in studying the properties of simplicial complexes. In 1998, Robin Forman developed gradient vector fields as a tool to study these complexes. Having gradient vector fields to study these...

Discrete Morse Theory Morse complex simplicial complex Strong Collapsibility Geometry and Topology mathematics Physical Sciences and Mathematics

In topology, simplicial complexes can be reduced to smaller complexes of the same simple homotopy type through a series of elementary collapses. It is a common goal to try to find the smallest complex that is of the same simple...

Discrete Morse Theory random strong topology Barmak Minian strong collapses simplicial complex mathematics Physical Sciences and Mathematics

The goal of this project is to construct a discrete Morse function which induces both a unique gradient vector field and homological sequence on a given tree. After reviewing the basics of discrete Morse theory, we will show...

Discrete Morse Theory Trees Gradient Vector Field Robin Forman Graph theory Forman equivalent algorithm Geometry and Topology mathematics