Efficient computations of discrete cubical homology

Fuente: arXiv
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Main Authors: Kapulkin, Chris, Kershaw, Nathan
Format: Preprint
Published: 2024
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author Kapulkin, Chris
Kershaw, Nathan
author_facet Kapulkin, Chris
Kershaw, Nathan
contents We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing literature, with the key insights including: a faster way to generate all singular cubes, reducing the dimensions of vector spaces in the chain complex by taking a quotient over automorphisms of the cube, and preprocessing graphs using the axiomatic treatment of discrete cubical homology.
format Preprint
id arxiv_https___arxiv_org_abs_2410_09939
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Efficient computations of discrete cubical homology
Kapulkin, Chris
Kershaw, Nathan
Computational Geometry
Algebraic Topology
Combinatorics
05-04, 05C25, 55U15
We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing literature, with the key insights including: a faster way to generate all singular cubes, reducing the dimensions of vector spaces in the chain complex by taking a quotient over automorphisms of the cube, and preprocessing graphs using the axiomatic treatment of discrete cubical homology.
title Efficient computations of discrete cubical homology
topic Computational Geometry
Algebraic Topology
Combinatorics
05-04, 05C25, 55U15
url https://arxiv.org/abs/2410.09939