Volume 13, issue 4 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The asymptotic behavior of least pseudo-Anosov dilatations

Chia-Yen Tsai

Geometry & Topology 13 (2009) 2253–2278
Abstract

For a surface S with n marked points and fixed genus g 2, we prove that the logarithm of the minimal dilatation of a pseudo-Anosov homeomorphism of S is on the order of log(n)n. This is in contrast with the cases of genus zero or one where the order is 1n.

Keywords
pseudo-Anosov dilatation, minimal translation length, mapping class group, Teichmuller space
Mathematical Subject Classification 2000
Primary: 37E30
Secondary: 57M99, 30F60
References
Publication
Received: 8 October 2008
Revised: 6 May 2009
Accepted: 29 March 2009
Published: 26 May 2009
Proposed: Joan Birman
Seconded: Danny Calegari, Walter Neumann
Authors
Chia-Yen Tsai
Department of Mathematics
The University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana, IL 61801
USA
http://www.math.uiuc.edu/~ctsai6/