Essential surfaces in graph pairs
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- by Henry Wilton
- J. Amer. Math. Soc. 31 (2018), 893-919
- DOI: https://doi.org/10.1090/jams/901
- Published electronically: June 18, 2018
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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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Bibliographic 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