Infinite presentations for fundamental groups of surfaces

2020/03/30 by Ryoma Kobayashi, Kobayashi, Ryoma
Mathematics · #20F05 #20F65 #57M05 #57M07 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2003.13224

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any finite type connected surface S, we give an infinite presentation of the fundamental group π₁(S,∗) of S based at an interior point ∗∈S whose generators are represented by simple loops. When S is non-orientable, we also give an infinite presentation of the subgroup of π₁(S,∗) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.

Citations

• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen
• A finite set of generators for the homeotopy group of a 2-manifold

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