# American Institute of Mathematical Sciences

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

## The relative cohomology of abelian covers of the flat pillowcase

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

Received  November 2014 Revised  March 2015 Published  June 2015

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.
Citation: Chenxi Wu. The relative cohomology of abelian covers of the flat pillowcase. Journal of Modern Dynamics, 2015, 9: 123-140. doi: 10.3934/jmd.2015.9.123
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##### References:
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