Combinatorial models for mapping class groups

Tara Brendle (University of Glasgow)

Monday 28th September, 2015 16:00-17:00 Maths 522


In 1997 Ivanov proved that the automorphism group of the complex of curves associated to a surface S is isomorphic to the (extended) mapping class group Mod(S), for most surfaces.  His work generated a flurry of activity, with similar results obtained by several different authors for various other simplicial complexes associated to surfaces.  Ivanov then posed a metaconjecture stating that every "sufficiently rich" complex associated to a surface S has Mod(S) as its group of automorphisms.  In this talk we will discuss a resolution of Ivanov's metaconjecture for a wide class of complexes and describe applications to normal subgroups of Mod(S).  (This is joint work with Dan Margalit.)

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