Article

Surface Subgroups of Graph Groups

Proceedings of the American Mathematical Society
Document Type

Article
Publication Date

7-1-1989
Disciplines

Abstract

Given a graph F, define the group Fr to be that generated by the vertices of F, with a defining relation xy = yx for each pair x, y of adjacent vertices of F. In this article, we examine the groups Fr, where the graph F is an n-gon, (n > 4). We use a covering space argument to prove that in this case, the commutator subgroup F.' contains the fundamental group of the orientable surface of genus 1 + (n - 4)2n-3 . We then use this result to classify all finite graphs F for which Fr is a free group.
DOI

10.2307/2047406
Publisher Statement

First published in Proceedings of the American Mathematical Society in 106(3), published by the American Mathematical Society.

Citation Information

Herman J. Servatius, Carl Droms and Brigitte Servatius. "Surface Subgroups of Graph Groups" *Proceedings of the American Mathematical Society*Vol. 106 Iss. 3 (1989) p. 573 - 578

Available at: http://works.bepress.com/herman_servatius/1/