GEOMETRICITY AND POLYGONALITY IN FREE GROUPS

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Gordon and Wilton recently proved that the double D of a free group F amalgamated along a cyclic subgroup C of F contains a surface group if a generator w of C satisfies a certain 3-manifold theoretic condition, called virtually geometricity. Wilton and the author defined the polygonality of w which also guarantees the existence of a surface group in D. In this paper, virtual geometricity is shown to imply polygonality up to descending to a finite-index subgroup of F. That the converse does not hold will follow from an example formerly considered by Manning.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2011
Language
English
Article Type
Article; Proceedings Paper
Keywords

SUBGROUPS; THEOREM; GRAPHS

Citation

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v.21, no.1-2, pp.235 - 256

ISSN
0218-1967
URI
http://hdl.handle.net/10203/98802
Appears in Collection
MA-Journal Papers(저널논문)
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