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Virtual geometricity is rare

Part of: Structure and classification of infinite or finite groups Low-dimensional topology Probabilistic methods in group theory

Published online by Cambridge University Press:  01 July 2015

Christopher H. Cashen  and
Jason F. Manning
Christopher H. Cashen
Affiliation:
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria email christopher.cashen@univie.ac.at
Jason F. Manning
Affiliation:
Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853, USA email jfmanning@math.cornell.edu

Abstract

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We present the results of computer experiments suggesting that the probability that a random multiword in a free group is virtually geometric decays to zero exponentially quickly in the length of the multiword. We also prove this fact.

MSC classification

Primary: 20E05: Free nonabelian groups 20P05: Probabilistic methods in group theory 57M10: Covering spaces
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 444 - 455
Copyright
© The Author(s) 2015 

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