Year: 2025
Type: article
Abstract: The mapping class group Γ g 1 \Gamma _g^1 of a closed orientable surface of genus g ≥ 1 g \geq 1 with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation preserving homeomorphisms of the circle. This inclusion pulls back the powers of the discrete universal Euler class producing classes E n ∈ H 2 n ( Γ g 1 ; Z ) E^n \in H^{2n}(\Gamma _g^1;\mathbb {Z}) for all n ≥ 1 n\geq 1 . In this paper we study the power n = g n=g , and prove: E g E^g is a torsion class which generates a cyclic subgroup of H 2 g ( Γ g 1 ; Z ) H^{2g}(\Gamma _g^1; \mathbb Z) whose order is a positive integer multiple of 4 g ( 2 g + 1 ) ( 2 g − 1 ) 4g(2g+1)(2g-1) .
DOI: 10.1090/tran/9491
Authors: Solomon Jekel, Rita Jiménez Rolland
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3407600875
OpenAlex ID: W4411084925