Event
Dmitry Tamarkin, Northwestern University
Monday, September 11, 2017 11:00to12:00
Axiomatic microlocal category
I am going to present a construction of an infinity stable category associated to a closed symplectic manifold whose symplectic form has integer periods. 听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). 听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}. 听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).
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Seminar G茅om茅trie et topologie/Geometry-Topology
PK-5115, 201 ave. Pr茅sident-Kennedy, UQAM