Linear representation stable bounds for the integral cohomology of pure mapping class groups

2019/01/08 by Rolland, Rita Jimenez · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1901.02134

Abstract

In this paper we study the integral cohomology of pure mapping class groups of surfaces, and other related groups and spaces, as 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 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.

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• Periodicity in the homology of moduli spaces of disconnected submanifolds

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