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Torsion at the Threshold for Mapping Class Groups
The mapping class group \({\Gamma}_g^ 1\) of a closed orientable surface of genus \(g \geq 1\) 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 univ...
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description | The mapping class group \({\Gamma}_g^ 1\) of a closed orientable surface of genus \(g \geq 1\) 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 \(\text{E}^n \in H^{2n}({\Gamma}_g^1;\mathbb{Z})\) for all \(n\geq 1\). In this paper we study the power \(n=g,\) and prove: \(\text{E}^g\) is a torsion class which generates a cyclic subgroup of \(H^{2g}({\Gamma}_g^1;\mathbb{Z})\) whose order is a positive integer multiple of \(4g(2g+1)(2g-1)\). |
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subjects | Mapping Subgroups |
title | Torsion at the Threshold for Mapping Class Groups |
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