Extending Homeomorphisms from 2-punctured Surfaces to Handlebodies
نویسندگان
چکیده
Let Hg be a genus g handlebody, and Tg = ∂Hg a closed connected orientable surface. In this paper we find a finite set of generators for Eg 2 , the subgroup of PMCG2(Tg) consisting of the isotopy classes of homeomorphisms of Tg which admit an extension to the handlebody 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 Eg 2 in PMCG2(Tg) are equivalent. Mathematics Subject Classification 2000: Primary 20F38; Secondary 57M25, 57N10.
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