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Axiomatic microlocal category.

Banff International Research Station for Mathematical Innovation and Discovery

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 define 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 micro local category on M as hom(P,F_M).

Mathematics; Category theory; homological algebra; Quantum theory; Mathematical physics

video/mp4

Author affiliation: Northwestern University

2017-12-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63830

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/