The mapping class groups of reducible Heegaard splittings of genus two

2017/02/17 by Sangbum Cho, Cho, Sangbum, Yuya Koda +1
Mathematics · #57M60 #57N10 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.05306

openalex publication_date 2017/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, \mathbbS² × \mathbbS¹, lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the genus-2 splitting was shown to be finitely presented. In this work, we study the remaining generic lens spaces, and show that the mapping class group of the genus-2 Heegaard splitting is finitely presented for any lens space by giving its explicit presentation. As an application, we show that the fundamental groups of the spaces of the genus-2 Heegaard splittings of lens spaces are all finitely presented.

Citations

• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting

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