## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Rita Jiménez Rolland

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 5 (2019), 641-658.

Dates
First available in Project Euclid: 19 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1579402815

Digital Object Identifier
doi:10.36045/bbms/1579402815

Mathematical Reviews number (MathSciNet)
MR4053846

Zentralblatt MATH identifier
07167749

#### Citation

Jiménez Rolland, Rita. Linear representation stable bounds for the integral cohomology of pure mapping class groups. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 5, 641--658. doi:10.36045/bbms/1579402815. https://projecteuclid.org/euclid.bbms/1579402815