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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Essential surfaces in graph pairs
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by Henry Wilton HTML | PDF
J. Amer. Math. Soc. 31 (2018), 893-919 Request permission

Abstract:

A well-known question of Gromov asks whether every one-ended hyperbolic group $\Gamma$ has a surface subgroup. We give a positive answer when $\Gamma$ is the fundamental group of a graph of free groups with cyclic edge groups. As a result, Gromov’s question is reduced (modulo a technical assumption on 2-torsion) to the case when $\Gamma$ is rigid. We also find surface subgroups in limit groups. It follows that a limit group with the same profinite completion as a free group must in fact be free, which answers a question of Remeslennikov in this case.
References
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Additional Information
  • Henry Wilton
  • Affiliation: DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • MR Author ID: 814406
  • Email: h.wilton@maths.cam.ac.uk
  • Received by editor(s): January 15, 2017
  • Received by editor(s) in revised form: March 14, 2018
  • Published electronically: June 18, 2018
  • Additional Notes: The author was supported by EPSRC Standard Grant EP/L026481/1.
  • © Copyright 2018 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 31 (2018), 893-919
  • MSC (2010): Primary 20F65, 20F67, 57M07
  • DOI: https://doi.org/10.1090/jams/901
  • MathSciNet review: 3836561