Document Type

Article

Article Version

Publisher's PDF

Publication Date

2-2011

Abstract

A conjecture of Gromov states that a one-ended word-hyperbolic group must contain a subgroup that is isomorphic to the fundamental group of a closed hyperbolic surface. Recent papers by Gordon and Wilton and by Kim and Wilton give sufficient conditions for hyperbolic surface groups to be embedded in a hyperbolic Baumslag double G. Using Nielsen cancellation methods based on techniques from previous work by the second author, we prove that a hyperbolic orientable surface group of genus 2 is embedded in a hyperbolic Baumslag double if and only if the amalgamated word W is a commutator: that is, W = [U, V] for some elements U, V is an element of F. Furthermore, a hyperbolic Baumslag double G contains a non-orientable surface group of genus 4 if and only if W = X(2)Y(2) for some X, V is an element of F. G can contain no non-orientable surface group of smaller genus.

Comments

Copyright 2011 by Cambridge University Press. Original published version can be found at DOI: 10.1017/S0013091509001102

Publication Title

Proceedings of the Edinburgh Mathematical Society

Published Citation

B. Fine, and G. Rosenberger. Surface Groups Within Baumslag Doubles, Proceedings of the Edinburgh Mathematical Society. 54 (Part I), 91-97.

DOI

10.1017/S0013091509001102

Peer Reviewed

Download

Share

COinS