Local Poincaré duality, pre-CY structures and the categorical neighborhood of infinity [Bonn symplectic geometry seminar]

In this talk, I will explain how to produce, for any homology manifold with local Poincaré duality, a pre-Calabi-Yau structure on a certain category associated to it. This type of structure can be seen as a noncommutative analog of a Poisson bivector field, and the relevant category is a simplicial model for the chains on path spaces. Using this, one can define many operations on a certain Hochschild complex with values in Efimov’s categorical formal punctured neighborhood of infinity, which in the case of a manifold is a model for the Rabinowitz Floer cohomology of its cotangent bundle; these should be understood as algebraic incarnations of string topology operations of Chas-Sullivan-Goresky-Hingston and also of Floer-theoretic constructions of Cieliebak-Latschev-Oancea. This is joint work with Manuel Rivera and Zhengfang Wang.