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SUMMARY:Quantum cohomology of twistor spaces - Jonny Evans\, ETH Zurich
DTSTART:20111026T150000Z
DTEND:20111026T160000Z
UID:TALK32362@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Monotone symplectic (aka symplectic Fano) manifolds are pretty
  rare in the universe of all symplectic manifolds\, in much the same way t
 hat Fano varieties or Ricci-positive manifolds are rare. Positivity usuall
 y has strong implications for the underlying topology and one wonders if t
 he same is true here. However\, the twistor space of a hyperbolic 2n-manif
 old M (n bigger than or equal to 3) was observed to be a monotone symplect
 ic manifold by Fine and Panov in 2009 and these examples counter many of o
 ne's expectations of what a symplectic Fano manifold ought to look like. W
 e explore the symplectic topology of these spaces (for the simplest case n
 =3) further by computing their quantum cohomology ring and the self-Floer 
 cohomology of certain natural (equally unexpected) monotone Lagrangian sub
 manifolds (Reznikov Lagrangians) associated to totally geodesic n-dimensio
 nal submanifolds of M. We will see evidence that there might be (yet more 
 unusual) Lagrangians hiding in these spaces that we haven't yet observed.\
 n
LOCATION:MR13
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