Goeritz groups of bridge decompositions

Abstract

For a bridge decomposition of a link in the $3$-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the $3$-sphere that preserve each of the bridge sphere and link setwise. After describing basic properties of this group, we discuss the asymptotic behavior of the minimal pseudo-Anosov entropies. This gives an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings of the $3$-sphere and the real projective space.

arXiv comment42 pages, 21 figures

References in corpus (6)

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• Powell moves and the Goeritz group
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