Distance and the Goeritz groups of bridge decompositions

TL;DR

This paper proves that high-distance bridge decompositions in 3-manifolds lead to finite Goeritz groups, linking geometric complexity to algebraic properties of the link.

Contribution

It establishes a new threshold (distance ≥ 6) ensuring the finiteness of the Goeritz group for bridge decompositions.

Findings

Distance ≥ 6 implies finite Goeritz group

Connects geometric complexity with algebraic symmetry groups

Provides criteria for finiteness in 3-manifold link decompositions

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.