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Some surface subgroups survive surgery. (English) Zbl 1009.57017
It is proved that if \(M\) is a hyperbolic 3-manifold with a single torus boundary component, then all but finitely many surgeries on \(M\) contain the fundamental group of a closed orientable surface of genus at least two.
Reviewer: Daryl Cooper

MSC:
57M50 General geometric structures on low-dimensional manifolds
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
57N10 Topology of general \(3\)-manifolds (MSC2010)
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