Journal of Modern Dynamics (JMD)

The relative cohomology of abelian covers of the flat pillowcase

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

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Chenxi Wu - Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853, United States (email)

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, Teichm├╝ller dynamics.
Mathematics Subject Classification:  Primary: 37D40; Secondary: 37E30.

Received: November 2014;      Revised: March 2015;      Available Online: June 2015.