The asymptotic behavior of least pseudo-Anosov dilatations

Tsai, Chia-Yen

doi:10.2140/gt.2009.13.2253

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The asymptotic behavior of least pseudo-Anosov dilatations

Chia-Yen Tsai

Geometry & Topology 13 (2009) 2253–2278

DOI: 10.2140/gt.2009.13.2253

Abstract

For a surface $S$ with $n$ marked points and fixed genus $g \geq 2$ , 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 $1 ∕ n$ .

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/

Volume 13, issue 4 (2009)