Floer cohomology and Platonic solids

2 December 2013
Yanki Lekili
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). We prove this Lagrangian is non-displaceable by Hamiltonian isotopies via computing its Floer cohomology over a field of non-zero characteristic. The computation depends on certain counts of holomorphic disks with boundary on the Lagrangian, which we explicitly identify. This is joint work in progress with Jonny Evans.
  • Geometry and Analysis Seminar