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Cellular techniques in homological stability 2: mapping class groups

Presented by: 
Alexander Kupers Harvard University
Date: 
Tuesday 4th December 2018 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
This is the second of two talks about joint work with S. Galatius and O Randal-Williams on applications higher-algebraic structures to homological stability. In it we apply the general theory to the example of mapping class groups of surfaces. After reproving Harer's stability result, I will explain how to prove the novel phenomenon of secondary homological stability; there are maps comparing the relative homology groups of the stabilization map for different genus and there are isomorphisms in a range tending to infinity with the genus.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons