Generating the genus g+1 Goeritz group of a genus g handlebody

2011/08/23 by Martin Scharlemann, Scharlemann, Martin
Computer Science · Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1108.4671

27 pages, 8 figures

arxiv created 2011/08/23 · openalex publication_date 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A specific set of 4g+1 elements is shown to generate the Goeritz group of the genus g+1 Heegaard splitting of a genus g handlebody. These generators are consistent with Powell's proposed generating set for the Goeritz group of the genus g+1 splitting of S³. There are two proofs: one using purely classical techniques and one using thin position.

Related

• Powell moves and the Goeritz group
• Powell's Conjecture on the Goeritz group of S³ is stably true
• One Powell generator is redundant
• The genus two Goeritz group of S² × S¹
• Genus 2 Goeritz Equivalence in S³