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hal-00419939, version 1

## Hilden Braid Groups

Paolo Bellingeri () 1, Cattabriga Alessia () 2

(2009-09-25)

Abstract: 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.

• 1:  Laboratoire de Mathématiques Nicolas Oresme (LMNO)
• CNRS : UMR6139 – Université de Caen Basse-Normandie
• 2:  Università di Bologna (UNIBO)
• Università degli studi di Bologna
• Domain : Mathematics/Algebraic Topology
Mathematics/Geometric Topology
• Keywords : mapping class groups – extending homeomorphisms – handlebodies

• hal-00419939, version 1
• oai:hal.archives-ouvertes.fr:hal-00419939
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• Submitted on: Friday, 25 September 2009 21:20:11
• Updated on: Sunday, 4 October 2009 18:21:01