Abstract
Let Hgbe a genus g handlebody and MCG2n( Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg= ∂ Hg, fixing a given set of 2n points. In this paper we study two particular subgroups of MCG2n( Tg) which generalize Hilden groups defined by Hilden in [Generators for two groups related to the braid groups, Pacific J. Math.59 (1975) 475–486]. As well as Hilden groups are related to plat closures of braids, these generalizations are related to Heegaard splittings of manifolds and to bridge decompositions of links. Connections between these subgroups and motion groups of links in closed 3-manifolds are also provided.
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