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Goeritz groups of bridge decompositions

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arxiv 2004.03098 v1 pith:6WVCFCXS submitted 2020-04-07 math.GT

Susumu Hirose , Daiki Iguchi , Eiko Kin , Yuya Koda This is my paper · ORCID
classification math.GT
keywords spherebridgegoeritzgroupasymptoticbehaviorentropiesgroups
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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.

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