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Cohomology of braid groups and mapping class groups

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I will explain how “group completion” techniques lead to a description of the cohomology of braid groups(=spaces of configurations in the plane) and mapping class groups(=moduli spaces of Riemann surfaces). I hope to explain the method completely for braid groups, and indicate what one needs to worry about for mapping class groups. I will then survey explicit calculational information which can be obtained from this method (and others).

This talk is part of the Isaac Newton Institute Seminar Series series.

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