Abstract
In this paper we study the integral cohomology of pure mapping class groups of surfaces, and other related groups and spaces, as $\mathsf{FI}$-modules. We use recent results from Church, Miller, Nagpal and Reinhold to obtain explicit linear bounds for their presentation degree and to give an inductive description of these $\mathsf{FI}$-modules. Furthermore, we establish new results on representation stability, in the sense of Church and Farb, for the rational cohomology of pure mapping class groups of non-orientable surfaces.
Citation
Rita Jiménez Rolland. "Linear representation stable bounds for the integral cohomology of pure mapping class groups." Bull. Belg. Math. Soc. Simon Stevin 26 (5) 641 - 658, december 2019. https://doi.org/10.36045/bbms/1579402815
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