ettirapp / computational-topology

Computational Topology

These are some projects from a computational topology course given in Spring 2020. The projects are based on Herbert Edelsbrunner and J Harer's Computational Topology : An Introduction.

The three main components of the code:

Triangulation

Triangulation.py is a data structure to represent a triangulation. It takes triangles as input and forms them into a graph that represents the triangulation. The code determines the manifold's Euler characteristic, genus, and specific name of the manifold if it has one.

Simplicial Complex & Boundary Matrix

SimplicialComplex.py takes a simplex as input and forms it into a multi-dimensional simplicial complex. The code then calculates the boundary matrix for each dimension of the complex.

Persistent Homology

PersistentHomology.py is an algorithm to compute the persistent homology of a manifold from its boundary matrix.