Minimal pseudo-Anosov translation lengths on the complex of curves

Gadre, Vaibhav; Tsai, Chia-Yen

doi:10.2140/gt.2011.15.1297

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Minimal pseudo-Anosov translation lengths on the complex of curves

Vaibhav Gadre and Chia-Yen Tsai

Geometry & Topology 15 (2011) 1297–1312

DOI: 10.2140/gt.2011.15.1297

Abstract

We establish bounds on the minimal asymptotic pseudo-Anosov translation lengths on the complex of curves of orientable surfaces. In particular, for a closed surface with genus $g \geq 2$ , we show that there are positive constants $a_{1} < a_{2}$ such that the minimal translation length is bounded below and above by $a_{1} ∕ g^{2}$ and $a_{2} ∕ g^{2}$ .

Keywords

mapping class group, pseudo-Anosov map, complex of curves, Teichmüller

Mathematical Subject Classification 2010

Primary: 30F60, 32G15

References

Publication

Received: 18 January 2011

Revised: 18 June 2011

Accepted: 21 June 2011

Published: 29 July 2011

Proposed: Joan Birman

Seconded: David Gabai, Walter Neumann

Authors

Vaibhav Gadre
Department of Mathematics Harvard University Cambridge MA 02138 USA
http://www.math.harvard.edu/~vaibhav
Chia-Yen Tsai
Department of Mathematics University of Illinois Urbana-Champaign Urbana IL 61801 USA
http://www.math.uiuc.edu/~ctsai6

Volume 15, issue 3 (2011)