The relative cohomology of abelian covers of the  flat pillowcase

Chenxi  Wu

doi:10.3934/jmd.2015.9.123

Article Contents

2015, Volume 9: 123-140. Doi: 10.3934/jmd.2015.9.123

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The relative cohomology of abelian covers of the flat pillowcase

Chenxi Wu^1,

1.
Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853

Received: November 2014

Revised: March 2015

Published: May 2015

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Abstract

We calculate the action of the group of affine diffeomorphisms on the relative cohomology of pair $(M,\Sigma)$, where $M$ is a square-tiled surface that is a normal abelian cover of the flat pillowcase. As an application, we answer a question raised by Smillie and Weiss.

Keywords:

Square-tiled translation surface,
Teichmüller dynamics.

Mathematics Subject Classification: Primary: 37D40; Secondary: 37E30.

Citation:

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