Mapping class groups and function spaces: a survey

Abstract

This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of low-genus orientable and non-orientable surfaces.

References in corpus (10)

• Homological stability for the mapping class groups of non-orientable surfaces
• Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map
• The structure of the tautological ring in genus one
• The Gorenstein conjecture fails for the tautological ring of ${\bar{\mathcal{M}}}_{2,n}$
• Embeddings of the braid groups of covering spaces, classification of the finite subgroups of the braid groups of the real projective plane, and linearity of braid groups of low-genus surfaces
• A short exposition of the Madsen-Weiss theorem
• A presentation for the mapping class group of a nonorientable surface
• Different versions of mapping class groups of surfaces
• Farrell cohomology of low genus pure mapping class groups with punctures
• The space of immersed surfaces in a manifold