Goeritz groups of bridge decompositions

Susumu Hirose; Daiki Iguchi; Eiko Kin; Yuya Koda

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arXiv · 2004.03098

Goeritz groups of bridge decompositions

Susumu Hirose·Daiki Iguchi·Eiko Kin·Yuya Koda

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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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Susumu Hirose, Daiki Iguchi, Eiko Kin, Yuya Koda. 2020-04-07. Goeritz groups of bridge decompositions. https://arxiv.org/abs/2004.03098

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