Extending homeomorphisms from 2-punctured surfaces to handlebodies

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Let F a closed connected orientable surface bounding a genus g handlebody H. In this paper we find a finite set of generators for the subgroup E(2,g) of the pure mapping class group of the twice punctured torus PMCG(2,g), consisting of the isotopy classes of homeomorphisms of F which admit an extension to H keeping a properly embedded trivial arc fixed. This subgroup turns out to be important for the study of knots in closed 3-manifolds via (g,1)-decomposition. In fact, the knots represented by the isotopy classes belonging to the same left cosets of E(2,g) in PMCG(2,g) are equivalent.
9 pages, 5 figures

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Geometric Topology, 20F38; 57M25

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http://salesiana.dossiersoluciones.com/handle/123456789/107501

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601255
 http://arxiv.org/abs/math/0601255

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arXiv