# Commensurator subgroups of surface groups

Ocampo Uribe, Oscar Eduardo (2012) Commensurator subgroups of surface groups. Revista Colombiana de Matemáticas; Vol. 44, núm. 1 (2010); 1-13 0034-7426 .

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## Resumen

Let $M$ be a surface, and let $H$ be a subgroup of $\pi_{1}M$. In this paper we study the commensurator subgroup $C_{\pi_{1}M}(H)$ of $\pi_{1}M$, and we extend a result of L. Paris and D. Rolfsen \cite{Paris-Rolfsen}, when $H$ is a geometric subgroup of $\pi_{1}M$. We also give an application of commensurator subgroups to group representation theory. Finally, by considering certain closed curves on the Klein bottle, we apply a classification of these curves to self-intersection Nielsen theory.

Tipo de documento:Artículo - Article
Palabras clave:Commensurator, Fundamental group, Surface, 20F65, 57M05