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JMD

We study infinite translation surfaces which are $\ZZ$-covers of finite
square-tiled surfaces obtained by a certain

*two-slit cut and paste construction*. We show that if the finite translation surface has a one-cylinder decomposition in some direction, then the Veech group of the infinite translation surface is either a lattice or an infinitely generated group of the first kind. The square-tiled surfaces of genus two with one zero provide examples for finite translation surfaces that fulfill the prerequisites of the theorem.## Year of publication

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