Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two - II

2009/02/07 by Kim, Jungsoo
Mathematics · #57M99 #57S17 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0902.1241

openalex publication_date 2009/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed orientable 3-manifold with a genus two Heegaard splitting (V₁, V₂; F) and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and V_i are not ∂-parallel in V_i for i=1,2. If G is a finite group of orientation-preserving smooth actions on M which preserves each handlebody of the Heegaard splitting and each piece of the JSJ-decomposition of M, then G≅ ℤ₂ or \mathbbD₂ unless V_j∩(∪ T_i) has three or more disk components for j=1 or 2.

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