Random Simple-Homotopy Theory
Computational Geometry
2021-09-28 v2 Algebraic Topology
Combinatorics
Geometric Topology
Abstract
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 < 7, 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, (14k+1)-vertex triangulations of Bing's houses with k rooms, which all can be deformed to a point using only six pure elementary expansions.
Cite
@article{arxiv.2107.09862,
title = {Random Simple-Homotopy Theory},
author = {Bruno Benedetti and Crystal Lai and Davide Lofano and Frank H. Lutz},
journal= {arXiv preprint arXiv:2107.09862},
year = {2021}
}
Comments
23 pages, 6 figures, 5 tables