Surface subgroups from linear programming

@article{Calegari2015SurfaceSF,
  title={Surface subgroups from linear programming},
  author={Danny Calegari and Alden K. Walker},
  journal={Duke Mathematical Journal},
  year={2015},
  volume={164},
  pages={933-972}
}
  • Danny Calegari, Alden K. Walker
  • Published 2015
  • Mathematics
  • Duke Mathematical Journal
  • We show that a random endomorphism of a free group gives rise to an HNN extension which contains a closed surface subgroup, with probability one; a special case is the HNN extension associated to the endomorphism of a rank 2 free group (considered by Sapir) sending a to ab and b to ba. We further show that a group obtained by doubling a free group along any collection of subgroups (of arbitrary rank) has the property that every rational 2-dimensional homology class is virtually represented by… CONTINUE READING
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