Random simple-homotopy theory

We implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary...

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Bibliographic Details
Published inJournal of applied and computational topology Vol. 8; no. 3; pp. 531 - 555
Main Authors Benedetti, Bruno, Lai, Crystal, Lofano, Davide, Lutz, Frank H.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2024
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Summary:We implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions . For triangulated d -manifolds with d ≤ 6 , we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, ( 14 k + 1 ) -vertex triangulations of a new series of Bing’s houses with k rooms, k ≥ 3 , which all can be deformed to a point using only six pure elementary expansions.
ISSN:2367-1726
2367-1734
DOI:10.1007/s41468-023-00139-4