Finite presentations for the balanced superelliptic mapping class groups

2022/03/25 by Susumu Hirose, Hirose, Susumu, Genki Omori +1 · 1 citation
Mathematics · #20F05 #57M05 #57M07 #57S05 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2203.13413

openalex publication_date 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering space in the mapping class group of the total surface. We give finite presentations for the balanced superelliptic mapping class groups of closed surfaces, surfaces with one marked point, and surfaces with one boundary component. To give these presentations, we construct finite presentations for corresponding liftable mapping class groups in a different generating set from Ghaswala-Winarski's presentation in \citeGhaswala-Winarski1.

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• Liftable mapping class groups of certain branched covers of torus

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