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Random Möbius–Kantor group cobordisms

Sylvain Barré and Mikaël Pichot

Vol. 19 (2022), No. 4, 137–152

We introduce a new model of random groups, in which the random group is CAT (0) (but not hyperbolic). The definition relies on a surgery type construction for Möbius–Kantor complexes; it depends on the existence of a sufficiently large semigroup of group cobordisms, which can be composed in a random way to define a group. By construction, the local geometry in this model is preassigned. We aim to study the asymptotic geometry of the random group, in particular to prove that it is not hyperbolic in a strong sense.

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nonpositive curvature, discrete groups, random groups
Mathematical Subject Classification
Primary: 20F65
Received: 24 July 2021
Revised: 23 April 2022
Accepted: 25 August 2022
Published: 1 December 2022
Sylvain Barré
UMR 6205, Laboratoire de mathématiques de Bretagne Atlantique (LMBA)
Université Bretagne-Sud
Mikaël Pichot
Department of Mathematics and Statistics
McGill University
Montreal, QC