An alternative approach to extending pseudo-Anosovs over compression bodies

Ackermann, Robert

doi:10.2140/agt.2015.15.2383

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An alternative approach to extending pseudo-Anosovs over compression bodies

Robert Ackermann

Algebraic & Geometric Topology 15 (2015) 2383–2391

DOI: 10.2140/agt.2015.15.2383

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

Volume 15, issue 4 (2015)