Author:
Benedetti Bruno,Lai Crystal,Lofano Davide,Lutz Frank H.
Abstract
AbstractWe 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 $$d\le 6$$
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, $$(14k+1)$$
(
14
k
+
1
)
-vertex triangulations of a new series of Bing’s houses with k rooms, $$k\ge 3$$
k
≥
3
, which all can be deformed to a point using only six pure elementary expansions.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology