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Torus Surgery Constraints and Intermediate Covers of the Cartwright--Steger Surface
We study torus surgery on the Cartwright--Steger surface and the degree-two cover construction proposed in \cite[Remark~1]{ASY}. Every torus in this surface is integrally nullhomologous, and surgery on a fixed disjoint collection of such tori cannot decrease the first Betti number. We then determine
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