Hyperbolic surface subgroups of one-ended doubles of free groups

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Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group has a hyperbolic surface subgroup if (1) the free group has rank 2 or (2) every generator is used the same number of times in a minimal automorphic image of the amalgamating words. To prove this, we formulate a stronger statement on Whitehead graphs and prove its specialization by combinatorial induction for (1) and the characterization of perfect matching polytopes by Edmonds for (2).
Publisher
OXFORD UNIV PRESS
Issue Date
2014-12
Language
English
Article Type
Article
Citation

JOURNAL OF TOPOLOGY, v.7, no.4, pp.927 - 947

ISSN
1753-8416
DOI
10.1112/jtopol/jtu004
URI
http://hdl.handle.net/10203/201063
Appears in Collection
MA-Journal Papers(저널논문)
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