Mapping class groups and function spaces: a survey
Fred R. Cohen, Miguel A. Maldonado

TL;DR
This survey explores the connections between mapping class groups, configuration spaces, and function spaces, focusing on cohomology calculations for low-genus surfaces to understand their algebraic and topological properties.
Contribution
It compiles and reviews existing calculations of cohomology groups for mapping class groups of low-genus surfaces, highlighting their relationships with configuration and function spaces.
Findings
Cohomology groups for low-genus orientable surfaces are systematically calculated.
Cohomology groups for non-orientable surfaces are also analyzed.
The survey consolidates key results linking mapping class groups with configuration and function spaces.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Algebra and Geometry
