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The Dehn function and a regular set of normal forms for R. Thompson's group F

Part of: Low-dimensional topology Connections with homological algebra and category theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

V. S. Guba  and
M. V. Sapir
V. S. Guba
Affiliation:
Department of Mathematics Vologda State Pedagogical InstituteS. Orlov Street 6 160600, VologdaRussia e-mail: guba@vgpi.vologda.su
M. V. Sapir
Affiliation:
Department of Mathematics and Statistics University of Nebraska-LincolnCenter for Communication and Information Science Lincoln, NE 68588-0323USA e-mail: mvs@unlinfo.unl.edu
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Abstract

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We show that the group F discovered by Richard Thompson in 1965 has a subexponential upper bound for its Dehn function. This disproves a conjecture by Gersten. We also prove that F has a regular terminating confluent presentation.

MSC classification

Secondary: 20J05: Homological methods in group theory 20F06: Cancellation theory; application of van Kampen diagrams 20F10: Word problems, other decision problems, connections with logic and automata 57M07: Topological methods in group theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 315 - 328
Copyright
Copyright © Australian Mathematical Society 1997

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