Floer cohomology and Platonic Solids

Yanki Lekili (King's College London)

Wednesday 26th March, 2014 15:30-16:30 Maths 325


We consider Fano threefolds on which SL(2,C) acts with a
 dense open orbit. This is a finite list of threefolds whose
 classification follows from the classical work of Mukai-Umemura and
 Nakano. Inside these threefolds, there sits a Lagrangian space form
 given as an orbit of SU(2). I will discuss the interesting case of a
 Lagrangian SU(2)/D_6 in CP^3. We prove this Lagrangian is
 non-displaceable by Hamiltonian isotopies via computing its Floer
 cohomology over a field of characteristic 5 and that it (strongly)
 generates the Fukaya category of CP^3 as a triangulated category (which in particular implies that
 it is non-displaceable from any other object of the Fukaya category,
 such as the Clifford torus). The computation depends on certain counts
 of holomorphic disks with boundary on the Lagrangian, which we
 explicitly identify. This is joint work with Jonny Evans.

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