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Abstract: Gordon and Wilton recently proved that the double D of a free group Famalgamated along a cyclic subgroup C of F contains a surface group if agenerator w of C satisfies a certain 3-manifold theoretic condition, calledvirtually geometricity. Wilton and the author defined the polygonality of wwhich also guarantees the existence of a surface group in D. In this paper,virtual geometricity is shown to imply polygonality up to descending to afinite-index subgroup F- and applying an automorphism on F-. That the conversedoes not hold will follow from an example formerly considered by Manning.



Author: Sang-hyun Kim

Source: https://arxiv.org/







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