Torsion at the Threshold for Mapping Class Groups

2024/09/11 by Solomon M. Jekel, Jekel, Solomon, Rita Jiménez Rolland +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2409.07311

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The mapping class group Γ_g^ 1 of a closed orientable surface of genus g ≥ 1 with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation preserving homeomorphims of the circle. This inclusion pulls back the powers of the discrete universal Euler class producing classes Eⁿ ∈ H²ⁿ(Γ_g¹;ℤ) for all n≥ 1. In this paper we study the power n=g, and prove: E^g is a torsion class which generates a cyclic subgroup of H^2g(Γ_g¹;ℤ) whose order is a positive integer multiple of 4g(2g+1)(2g-1).

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