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Bounding genera of singular surfaces

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NPC - Non-positive curvature group actions and cohomology

If two simple closed curves on a closed surface lie in the same non-trivial homology class, then they bound a singular orientable surface. One can relate the minimal genus of such to distances in the curve graph. I will describe this, and some related results. The proofs are not hard, but call for some non-trivial input.  Maybe there is a simple combinatorial argument.



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