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Random Möbius–Kantor
group cobordisms
Sylvain Barré and Mikaël Pichot |
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Vol. 19 (2022), No. 4, 137–152
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Abstract |
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We introduce a new model of random groups, in which the random group is (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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Keywords
nonpositive curvature, discrete groups, random groups
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Mathematical Subject Classification
Primary: 20F65
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Milestones
Received: 24 July 2021
Revised: 23 April 2022
Accepted: 25 August 2022
Published: 1 December 2022
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Authors |
| Sylvain Barré | |
| UMR 6205, Laboratoire de
mathématiques de Bretagne Atlantique (LMBA) Université Bretagne-Sud Vannes France |
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| Mikaël Pichot | |
| Department of Mathematics and
Statistics McGill University Montreal, QC Canada |
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