Infinitely many lattice surfaces with special pseudo-Anosov maps

Kariane Calta; Thomas A. Schmidt

doi:10.3934/jmd.2013.7.239

Article Contents

2013, Volume 7, Issue 2: 239-254. Doi: 10.3934/jmd.2013.7.239

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Infinitely many lattice surfaces with special pseudo-Anosov maps

Kariane Calta^1, and
Thomas A. Schmidt^2,

1.
Vassar College, Poughkeepsie, NY 12604-0257
2.
Oregon State University, Corvallis, OR 97331

Received: September 30, 2012

Revised: April 30, 2013

Published: August 2013

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Abstract

We give explicit pseudo-Anosov homeomorphisms with vanishing Sah-Arnoux-Fathi invariant. Any translation surface whose Veech group is commensurable to any of a large class of triangle groups is shown to have an affine pseudo-Anosov homeomorphism of this type. We also apply a reduction to finite triangle groups and thereby show the existence of nonparabolic elements in the periodic field of certain translation surfaces.

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Mathematics Subject Classification: Primary: 37D99; Secondary: 30F60, 37A25, 37A45, 37F99, 58F15.

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