Hilden Braid Groups

Paolo Bellingeri; Cattabriga Alessia

Hilden Braid Groups

Algebraic Topology 2009-10-04 v1 Geometric Topology

Authors: Paolo Bellingeri , Cattabriga Alessia

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

heegaard splittings braid groups

Cite

@article{arxiv.0909.4845,
  title  = {Hilden Braid Groups},
  author = {Paolo Bellingeri and Cattabriga Alessia},
  journal= {arXiv preprint arXiv:0909.4845},
  year   = {2009}
}

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