All Title Author
Keywords Abstract

Mathematics  2009 

Geometricity and Polygonality in Free Groups

Full-Text   Cite this paper   Add to My Lib


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 F' and applying an automorphism on F'. That the converse does not hold will follow from an example formerly considered by Manning.


comments powered by Disqus

Contact Us


微信:OALib Journal