Galois Action on Homology of the Heisenberg Curve

2024/11/17 by Aristides Kontogeorgis, Kontogeorgis, Aristides, Dimitrios Noulas +1
Computer Science · Mathematics · #11G30 #14H37 #20F36 #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2411.11140

openalex publication_date 2024/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Heisenberg curve is defined topologically as a cover of the Fermat curve and corresponds to an extension of the projective line minus three points by the non-abelian Heisenberg group modulo n. We compute its fundamental group and investigate an action from Artin's Braid group to the curve itself and its homology. We also provide a description of the homology in terms of irreducible representations of the Heisenberg group over a field of characteristic 0.

Related

• Galois action on the homology of Fermat curves
• Galois action on homology of generalized Fermat Curves
• The group of automorphisms of the Heisenberg curve
• Heisenberg homology on surface configurations
• The Galois action and cohomology of a relative homology group of Fermat\n Curves