Quantum cohomology of twistor spaces

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• Jonny Evans, ETH Zurich
• Wednesday 26 October 2011, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Monotone symplectic (aka symplectic Fano) manifolds are pretty rare in the universe of all symplectic manifolds, in much the same way that Fano varieties or Ricci-positive manifolds are rare. Positivity usually has strong implications for the underlying 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 observed to be a monotone symplectic manifold by Fine and Panov in 2009 and these examples counter many of one’s expectations of what a symplectic Fano manifold ought to look like. We 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 submanifolds (Reznikov Lagrangians) associated to totally geodesic n-dimensional 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.

This talk is part of the Differential Geometry and Topology Seminar series.

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