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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Quantum cohomology of twistor spaces - Jonny Evans
\, ETH Zurich
DTSTART;TZID=Europe/London:20111026T160000
DTEND;TZID=Europe/London:20111026T170000
UID:TALK32362AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32362
DESCRIPTION:Monotone symplectic (aka symplectic Fano) manifold
s are pretty rare in the universe of all symplecti
c manifolds\, in much the same way that Fano varie
ties or Ricci-positive manifolds are rare. Positiv
ity usually has strong implications for the underl
ying topology and one wonders if the same is true
here. However\, the twistor space of a hyperbolic
2n-manifold M (n bigger than or equal to 3) was ob
served to be a monotone symplectic manifold by Fin
e and Panov in 2009 and these examples counter man
y of one's expectations of what a symplectic Fano
manifold ought to look like. We explore the symple
ctic topology of these spaces (for the simplest ca
se n=3) further by computing their quantum cohomol
ogy ring and the self-Floer cohomology of certain
natural (equally unexpected) monotone Lagrangian s
ubmanifolds (Reznikov Lagrangians) associated to t
otally geodesic n-dimensional submanifolds of M. W
e will see evidence that there might be (yet more
unusual) Lagrangians hiding in these spaces that w
e haven't yet observed.\n
LOCATION:MR13
CONTACT:Ivan Smith
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