Genus three Goeritz groups of connected sums of two lens spaces

TL;DR

This paper proves that the mapping class groups of genus 3 Heegaard splittings for connected sums of two lens spaces are finitely generated and their reducing sphere complexes are connected.

Contribution

It establishes the finite generation and connectivity of the reducing sphere complexes for these specific 3-manifold splittings.

Findings

Mapping class groups are finitely generated.

Reducing sphere complexes are connected.

Results apply to genus 3 splittings of connected sums of lens spaces.

Abstract

We prove that the mapping class groups of the genus 3 Heegaard splittings of the connected sum of two lens spaces are finitely generated, and the corresponding reducing sphere complexes are all connected.