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SUMMARY:COLLOQUIUM (Jour exceptionnel) Richard Hain: Mapping class groups 
 of simply connected algebraic manifolds
DTSTART:20230926T143000Z
DTEND:20230926T153000Z
DTSTAMP:20260423T141500Z
UID:indico-event-9892@indico.math.cnrs.fr
DESCRIPTION:Speakers: Richard Hain (Duke University)\n\nThe mapping class 
 group of an oriented manifold M is the group of connected components of it
 s group of orientation preserving diffeomorphisms. When M is a closed surf
 ace of genus g\, there is avery close (and classical) relation between the
  mapping class group and the moduli space of compact Riemann surfaces of g
 enus g that comes from Teichmuller theory. One manifestation of this relat
 ionship is that the (orbifold) fundamental group of the moduli space is is
 omorphic to the mapping class group of the surface.One can ask if this rel
 ation persists in higher dimensions. Surprisingly\, very little is known a
 nd the subject is in its infancy. In this talk\, after reviewing the class
 ical case\, I will discuss the problem of understanding mapping class grou
 ps of simply connected complex projective manifolds and then specialize to
  the case of hypersurfaces in projective (n+1)-space when n>2. The most de
 finitive results are due to Kreck and Su and apply when n=3. I will also e
 xplain why the mapping class group of a 3-dimensional hypersurface of degr
 ee > 3 is not isomorphic to the fundamental group of the corresponding mod
 uli space\, a consequence of the work of Kreck-Su and older work of Carlso
 n and Toledo.\n\nhttps://indico.math.cnrs.fr/event/9892/
LOCATION:René Baire (IMB)
URL:https://indico.math.cnrs.fr/event/9892/
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