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math.GTApr 7, 2001
34
citations (OpenAlex)
authors
  • D Cooper
  • D D Long
institutions
  • University of California, Santa Barbara
arXiv abstractPDF
paper

Some surface subgroups survive surgery

arXiv:math/0104088 · doi:10.2140/gt.2001.5.347

Abstract

It is shown that with finitely many exceptions, the fundamental group obtained by Dehn surgery on a one cusped hyperbolic 3-manifold contains the fundamental group of a closed surface.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper12.abs.html

Cited by in corpus (13)

  • The virtual Haken conjecture: Experiments and examples
  • Separation of Relatively Quasiconvex Subgroups
  • Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
  • A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
  • Problems In Groups, Geometry, and Three-Manifolds
  • Finite-volume Hyperbolic 3-Manifolds contain immersed Quasi-Fuchsian surfaces
  • Closed Quasi-Fuchsian Surfaces In Hyperbolic Knot Complements
  • Quasi-Fuchsian Surfaces In Hyperbolic Link Complements
  • Real places and torus bundles
  • Surface subgroups and handlebody attachment
  • Combination of fully quasiconvex subgroups and its applications
  • A combination theorem for Veech subgroups of the mapping class group
  • Singular surfaces, mod 2 homology, and hyperbolic volume, I
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