Mod \(p\) homology of the stable mapping class group. (English) Zbl 1074.57013

Galatius, Søren

Topology 43, No. 5, 1105-1132 (2004).

Let \(F_{g,n}\) be an oriented surface of genus \(g\) with \(n\) boundary components and let \(\Gamma_{g,n}\) denote the mapping class group of \(F_{g,n}\), the group of isotopy classes of orientation-preserving diffeomorphisms of \(F_{g,n}\) fixing each point in a neighborhood of the boundary of \(F_{g,n}\). In this paper the author calculates the homology groups \(H_*(F_{g,n};{\mathbb{F}}_p)\) in the stable range. The calculation is based on the proof of Mumford Conjecture given by I. Madsen and M. Weiss.

Reviewer: Mustafa Korkmaz (Ankara)

MSC:

57M99	General low-dimensional topology
57M50	General geometric structures on low-dimensional manifolds

Keywords:

mapping class groups; moduli spaces; Thom spectra; homology of infinite loop spaces