Higher rank local systems for monotone Lagrangians

Vendredi 28 avril 2017 14:00-15:00 - Momchil Konstantinov - UC London

Résumé : In this talk I will explain how one can naturally extend monotone Lagrangian Floer theory to the setting when the Lagrangians are equipped with local systems of rank higher than one. The presence of holomorphic discs of Maslov index 2 poses a potential obstruction to such an extension. However, for an appropriate choice of local systems the obstruction might vanish and, if not, one can always restrict to some natural unobstructed subcomplexes.
I will showcase all of these constructions with some explicit calculations for the Chiang Lagrangian in CP^3. Its Floer theory was computed by Evans and Likili, who also pointed out that standard Floer homology cannot tell us whether the Chiang Lagrangian and RP^3 can be disjoined by a Hamiltonian isotopy. We will see how using a rank 2 local system in this example allows us to show that these two Lagrangians are in fact non-displaceable.

Lieu : salle 121-123

Higher rank local systems for monotone Lagrangians  Version PDF