2017-geometrieSymplectique

I am going to present a construction of an infinity stable category associated to a closed symplectic manifold whose symplectic form has integer periods.  The category looks like the Fukaya category of M with coefficients in a certain local system. One first defines an infinity category C_{rR} associated to the product of two symplectic balls B_r times B_R whose objects are (roughly) graphs of symplectomorphic embeddings B_r to B_R and homs are positive isotopies (it is defined via listing axioms which characterize it).  We have a composition C_{r_1r_2} times C_{r_2r_3} to C_{r_1r_3} so that we have an infinity 2-category C whose 0-objects are balls and the category of morphisms between B_r and B_R is C_{rR}.  One has a functor F_M from C to the infinity 2 category of infinity categories, where F_M(B_r) is the category of symplectic embeddings B_r--> M. One also has another functor P between the same infinity categories and one defines the microlocal category on M as hom(P,F_M).

Location: UQAM, 201 ave. Président-Kennedy, PK-5115