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Finding simple curves in surface covers is undecidable. (English) Zbl 1467.57014

Summary: It is shown that various questions about the existence of simple closed curves in normal subgroups of surface groups are undecidable.

MSC:

57M10 Covering spaces and low-dimensional topology
57M05 Fundamental group, presentations, free differential calculus
57M07 Topological methods in group theory
57K20 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.)
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References:

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