Abstract

OCAMPO URIBE, OSCAR EDUARDO. Commensurator Subgroups of Surface Groups. Rev.colomb.mat. [online]. 2010, vol.44, n.1, pp.1-13. ISSN 0034-7426.

Let M be a surface, and let H be a subgroup of π₁M. In this paper we study the commensurator subgroup C_{\\pi_1M}(H) of π₁M, and we extend a result of L. Paris and D. Rolfsen [7], when H is a geometric subgroup of π₁M. 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.

Keywords : Commensurator; Fundamental group; Surface.

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