A note on large bounding and non-bounding finite group-actions on surfaces of small genus

2022/05/28 by Bruno Zimmermann, Zimmermann, Bruno P.
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.14425

openalex publication_date 2022/05/28 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

The classification of finite group-actions on closed surfaces of small genus is well-known. In the present paper we are interested in the question of which of these group-actions are bounding (extend to a compact 3-manifold with the surface as its unique boundary component, e.g. to a handlebody) or geometrically bounding (extend to a hyperbolic 3-manifold with totally geodesic boundary), concentrating, as a typical case, on large group-actions on surfaces of genus 3.

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