SL(2,ℤ), les tresses à trois brins et le tore modulaire

2022/12/20 by Alexis Marin, Marin, Alexis
Mathematics · #20-03 #20F05 #20F36 #20H05 #57-03 #57M07 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2212.10157

openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The action of SL(2,ℤ) on the integer torus and its quotient by central symmetry and Artin's presentation of three strings braids, produces a presentation with parabolic generators \pmatrix1& -1\cr 0& 1\cr and \pmatrix1& 0\cr 1& 1\cr and describes the action of the derived group on Poincaré's half plane.

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