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DESCRIPTION: A standard task in topology is to simplify a given finite pres
entation of a topological space. Bistellar flips allow to search for vertex
-minimal triangulations of surfaces or higher-dimensional manifolds\, and e
lementary collapses are often used to reduce a simplicial complex in size a
nd potentially in dimension. Simple-homotopy theory\, as introduced by Whit
ehead in 1939\, generalizes both concepts. We take on a random approach to
simple-homotopy theory and present a heuristic algorithm to combinatoriall
y deform non-collapsible\, but contractible complexes (such as triangulatio
ns of the dunce hat\, Bing's house or non-collapsible balls that contain sh
ort 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 L
ai\, and Frank Lutz.)
DTSTAMP:20210607T192300
DTSTART:20210614T144500
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Davide Lofano (Technische Universität Berlin): Random Simple-Homoto
py Theory
UID:107918297@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210614-C-Lofano.html
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