Constructing subdivision rules from polyhedra with identifications

Rushton, Brian

doi:10.2140/agt.2012.12.1961

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Constructing subdivision rules from polyhedra with identifications

Brian Rushton

Algebraic & Geometric Topology 12 (2012) 1961–1992

DOI: 10.2140/agt.2012.12.1961

Abstract

Cannon, Swenson and others have proved numerous theorems about subdivision rules associated to hyperbolic groups with a $2$ –sphere at infinity. However, few explicit examples are known. We construct an explicit finite subdivision rule for many $3$ –manifolds obtained from polyhedral gluings. The manifolds that satisfy the conditions include all manifolds created from compact right angled hyperbolic polyhedra, as well as many $3$ –manifolds with toral or hyperbolic boundary.

Keywords

finite subdivision rule, hyperbolic polyhedra

Mathematical Subject Classification 2010

Primary: 20F67, 57M50

References

Publication

Received: 24 January 2012

Revised: 5 June 2012

Accepted: 9 July 2012

Published: 27 October 2012

Authors

Brian Rushton
Department of Mathematics Temple University Room 638 Wachman Hall 1805 N. Broad Street Philadelphia, PA 19122 USA
https://sites.google.com/site/rushtonresearch/home

Volume 12, issue 4 (2012)