Distance and the Goeritz groups of bridge decompositions

Daiki Iguchi and Yuya Koda

Vol. 315 (2021), No. 2, 347–368

DOI: 10.2140/pjm.2021.315.347

Abstract

We prove that if the distance of a bridge decomposition of a link with respect to a Heegaard splitting of a $3$-manifold is at least $6$, then the Goeritz group is a finite group.

Keywords

bridge decomposition, curve complex, Goeritz group

Mathematical Subject Classification

Primary: 57K10, 57M60

Milestones

Received: 6 May 2021

Revised: 5 September 2021

Accepted: 11 October 2021

Published: 19 January 2022