Random SimpleHomotopy Theory
Abstract
We implement an algorithm RSHT (Random SimpleHomotopy) to study the simplehomotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higherdimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated dmanifolds 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 15vertex 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.09862
 Bibcode:
 2021arXiv210709862B
 Keywords:

 Computer Science  Computational Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 Mathematics  Geometric Topology;
 57Q10;
 57Q15
 EPrint:
 23 pages, 6 figures, 5 tables