Genus three Goeritz groups of connected sums of two lens spaces

2024/11/23 by Hao Chen, Chen, Hao, Yanqing Zou +1
Mathematics · #20F05 #57K20 #57K30 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2411.15471

openalex publication_date 2024/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The mapping class groups of reducible Heegaard splittings of genus two
• Connected primitive disk complexes and genus two Goeritz groups of lens spaces
• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
• The Goeritz group of a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients
• Haken spheres for genus two Heegaard splittings