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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
An alternative approach to extending pseudo-Anosovs over compression bodies

Robert Ackermann

Algebraic & Geometric Topology 15 (2015) 2383–2391
Abstract

Biringer, Johnson, and Minsky proved that any pseudo-Anosov whose stable lamination is the limit of disks in a compression body has a power which extends over some non-trivial minimal compression body. This paper presents an alternative proof of their theorem. The key ingredient is the existence of a certain collection of disks whose boundaries are formed from an arc of the stable lamination and an arc of the unstable lamination. The proof here also shows that there are only finitely many minimal compression bodies over which a power of a pseudo-Anosov can extend.

Keywords
pseudo-Anosov, compression bodies
Mathematical Subject Classification 2010
Primary: 57M99
References
Publication
Received: 24 June 2014
Revised: 6 November 2014
Accepted: 14 December 2014
Published: 10 September 2015
Authors
Robert Ackermann
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93106-3080
USA