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Algebra and Geometry Seminar

Thursday, October 5, 2023
2:30pm to 3:30pm
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Linde Hall 187
Lagrangian cobordism functor in microlocal sheaf theory
Wenyuan Li, Department of Mathematics, USC,

Consider the cosphere bundle of a manifold with the standard contact structure and Lagrangian cobordisms in its symplectization between Legendrian submanifolds. We construct a fully faithful functor between the categories of sheaves with singular support on the corresponding Legendrians, after enhancing the category at the negative end by local systems on the cobordism. In the special case where the contact manifold is the 1-jet bundle, we give a geometric model of the enhanced category as sheaves on the original manifold times the real line with microsupport on the cobordism. This gives a sheaf theoretic description of the maps between Legendrian contact homologies with coefficients enhanced by chains of the based loop spaces, defined using pseudoholomorphic curves.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].