Augmentation categories of Legendrian submanifolds.
Baptiste Chantraine (University of Nantes)
Monday 5th May, 2014 16:00-17:00 Maths 204
Legendrian submanifolds are submanifold in contact manifold. These arise naturally, for instance, as conormal spherical bundle of submanifolds on one side and as jet of functions on another. Chekanov algebra is a differential graded algebra associated to such Legendrian submanifolds which is a powerful invariant arising from symplectic field theory considerations. In order to extract finite dimensional invariants out of this DGA, Youri Chekanov developed the notion of linearisation which used the notion of augmentation. In this talk we will use the non-commutativity of Chekanov's DGA to define the notion of bilinearisation of Chekanov DGA using two augmentations. We will this that the resulting complexes are morphisms spaces of an A-infinity category called the Augmentation category. Time permitting we will describe how this category relates to a geometrical Fukaya type category and use this to distinguish non isotopic Lagrangian fillings of the trefoil Legendrian knot. This is a joint work with Frédéric Bourgeois.