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PRODID:-//Northeastern Topology Seminar//NONSGML v1.0//EN
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UID:208-0
SUMMARY:Andrea Bianchi: Mapping class group actions on configuration spaces and the Johnson filtration
DTSTART:20210420T160000Z
DTEND:20210420T170000Z
DTSTAMP:20210108T164820Z
LAST-MODIFIED:20210406T180000Z
SEQUENCE:0
DESCRIPTION:Abstract: This is joint work with Jeremy Miller and Jennifer Wilson. Let M be an orientable surface of genus g with one boundary curve\, and let F_n(M) denote the configuration space of n ordered points in M. The action of Homeo(M\,dM) on F_n(M) descends to an action of the mapping class group Gamma(M\,dM) on the homology H_*(F_n(M)). Our main result is that\, for all n\,i>=0\, the i-th stage J(i) of the Johnson's filtration of Gamma(M\,dM) acts trivially on H_i(F_n(M)). This extends previous work of Moriyama on certain relative configuration spaces.\nI will recall the necessary definitions and give a sketch of the proof of the main theorem: the main inputs are Moriyama's work and a cell stratification of F_n(M) à la Fox-Neuwirth-Fuchs. I will also present some examples of non-trivial actions of mapping classes in J(i-1) on elements of H_i(F_n(M))\, for small values of i.
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