Simplicial descent for Chekanov-Eliashberg dg-algebras

Simplicial descent for Chekanov-Eliashberg dg-algebras

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Johan Asplund, Columbia University
Fine Hall 314

In-Person and Online Talk

The Chekanov-Eliashberg dg-algebra gives an invariant of Legendrian submanifolds up to Legendrian isotopy and can be used to compute wrapped Fukaya categories of Weinstein manifolds. In this talk we introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. We will mainly discuss the result that the Chekanov-Eliashberg dg-algebra of the top attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. If time permits we will also touch on the subject of defining the Chekanov-Eliashberg dg-algebra for singular Legendrians and applications to knot contact homology for tangles.

This talk is partially based on joint work with Tobias Ekholm.