# Colloquium by Davide Lofano (Technische Universität Berlin): Random Simple-Homotopy Theory

A standard task in topology is to simplify a given finite presentation of

a topological space. Bistellar flips allow to search for vertex-minimal

triangulations of surfaces or higher-dimensional manifolds, and elementary

collapses are often used to reduce a simplicial complex in size and

potentially in dimension. Simple-homotopy theory, as introduced by

Whitehead in 1939, generalizes both concepts.

We take on a random approach to simple-homotopy theory and present a

heuristic algorithm to combinatorially deform non-collapsible, but

contractible complexes (such as triangulations of the dunce hat, Bing's

house or non-collapsible balls that contain short knots) to a point.

The procedure also allows to find substructures in complexes, e.g.,

surfaces in higher-dimensional manifolds or subcomplexes with torsion in

lens spaces.

(Joint work with Bruno Benedetti, Crystal Lai, and Frank Lutz.)

### Time & Location

Jun 14, 2021 | 02:45 PM

online