Strong accessibility for hyperbolic groups

Vavrichek, Diane M

doi:10.2140/agt.2008.8.1459

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Strong accessibility for hyperbolic groups

Diane M Vavrichek

Algebraic & Geometric Topology 8 (2008) 1459–1479

DOI: 10.2140/agt.2008.8.1459

Abstract

We use an accessibility result of Delzant and Potyagailo to prove Swarup’s Strong Accessibility Conjecture for Gromov hyperbolic groups with no $2$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn></math>$ –torsion. It follows that, if $M$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math>$ is an irreducible, orientable, compact $3$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn></math>$ –manifold with hyperbolic fundamental group, then any hierarchy in which $M$ $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math>$ is decomposed alternately along compressing disks and essential annuli is finite.

Keywords

group accessibility, hierarchies, hyperbolic groups, Bass–Serre theory

Mathematical Subject Classification 2000

Primary: 20E08, 20F65

Secondary: 57M99, 57N35, 20F67

References

Publication

Received: 17 August 2007

Revised: 12 December 2007

Accepted: 20 February 2008

Published: 5 September 2008

Authors

Diane M Vavrichek
Department of Mathematical Sciences Binghamton University Binghamton NY 13902-6000 USA
http://www.math.binghamton.edu/vavrichek/

Volume 8, issue 3 (2008)