Mapping class group action on the cohomology of the SLn character variety
Abstract
We describe the mapping class group action on the cohomology of the twisted SLn-character variety of a surface g of genus g. Our main tool is a relative version of the endoscopic decomposition of Maulik-Shen; this allows us to reduce the problem to the mapping class group action on the cohomology of a canonical finite cover of g, which was studied by Looijenga.
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