The fundamental group of compact Riemann surface

2023/11/19 by Yaacov Kopeliovich, Kopeliovich, Yaacov
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.11409

Abstract

We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle of the form (1...n) we derive a straightforward process to obtain the standard presentation of the fundamental group of Algebraic curve in the form ∏_i=1^g[a_i,b_i]=1

Related

• The Fundamental Group of a Compact Riemann Surface via Branched Covers
• Lectures on Klein surfaces and their fundamental group
• Fundamental groups of complements of curves as solvable groups
• The fundamental group of the complement of the branch curve of T times T in C²
• The action of the Mapping Class Group on the fundamental group of the complement of a finite subset of a Riemann surface of positive genus