# Hilden Braid Groups

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.
Keywords :
Document type :
Preprints, Working Papers, ...
2009
Domain :

https://hal.archives-ouvertes.fr/hal-00419939
Contributor : Paolo Bellingeri <>
Submitted on : Friday, September 25, 2009 - 9:20:11 PM
Last modification on : Sunday, October 4, 2009 - 6:21:01 PM
Document(s) archivé(s) le : Wednesday, June 16, 2010 - 12:08:14 AM

### Files

hildenarxiv.pdf
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### Identifiers

• HAL Id : hal-00419939, version 1
• ARXIV : 0909.4845

### Citation

Paolo Bellingeri, Cattabriga Alessia. Hilden Braid Groups. 2009. <hal-00419939>

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