Hilden Braid Groups

Paolo Bellingeri (1) , Cattabriga Alessia (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

Let $\H_g$ be a genus $g$ handlebody and $\MCG_{2n}(\T_g)$ be the $2n$-punctured mapping class group of $\T_g=\partial\H_g$. In this paper we study two particular subgroups of $\MCG_{2n}(\T_g)$ which generalize Hilden groups. As well as Hilden groups are related to plate 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.

Keywords: mapping class groups; extending homeomorphisms; handlebodies

Domains: Algebraic Topology [math.AT]; Geometric Topology [math.GT]

Paolo Bellingeri, Cattabriga Alessia. Hilden Braid Groups. 2009. ⟨hal-00419939⟩