Work

Morse Theoretic Templates for High Dimensional Homology Computation

Year: 2021

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2105.09870

Authors: Harker, Shaun, Mischaikow, Konstantin, Spendlove, Kelly

Institutions: Rutgers, The State University of New Jersey, University of Oxford

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3161836674

Cites: 11

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Related to: 10