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Morse Theoretic Templates for High Dimensional Homology Computation
- Publication Year :
- 2021
-
Abstract
- We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persistent homology, Conley complexes) of cell complexes. We demonstrate the effectiveness of templates in two settings: first, by computing the homology of certain cubical complexes which are homotopy equivalent to $\mathbb{S}^d$ for $1\leq d \leq 20$, and second, by computing Conley complexes and connection matrices for a collection of examples arising from a Conley-Morse theory on spaces of braids diagrams.<br />Comment: Updated timing information for improved version of PyCHomP
- Subjects :
- Mathematics - Algebraic Topology
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2105.09870
- Document Type :
- Working Paper