Let H g be a genus g handlebody and MCG 2n(T g) be the group of the isotopy classes of orientation preserving homeomorphisms of T g = ∂H g, fixing a given set of 2n points. In this paper we study two particular subgroups of MCG 2n(T g) which generalize Hilden groups defined by Hilden in [Generators for two groups related to the braid groups, Pacific J. Math. 59 (1975) 475486]. 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. © 2012 World Scientific Publishing Company.
Bellingeri, P., Cattabriga, A. (2012). Hilden braid groups. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 21(3), 1-22 [10.1142/S0218216511009534].
Hilden braid groups
CATTABRIGA, ALESSIA
2012
Abstract
Let H g be a genus g handlebody and MCG 2n(T g) be the group of the isotopy classes of orientation preserving homeomorphisms of T g = ∂H g, fixing a given set of 2n points. In this paper we study two particular subgroups of MCG 2n(T g) which generalize Hilden groups defined by Hilden in [Generators for two groups related to the braid groups, Pacific J. Math. 59 (1975) 475486]. 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. © 2012 World Scientific Publishing Company.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
