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The relative cohomology of abelian covers of the flat pillowcase

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


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