Simplicial descent for Chekanov-Eliashberg dg-algebras

December 17, 2021
In this talk we introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. We will discuss the result that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and there is in fact a one-to-one correspondence (up to Weinstein homotopy) between simplicial decompositions and so-called good sectorial covers. The motivation behind these results is the sectorial descent result for wrapped Fukaya categories by Ganatra-Pardon-Shende.