Lagrangianska delmångfold, Algebraisk K-teori och Kvantefysik
Tidsperiod: 2018-12-01 till 2021-12-31
Projektledare: Thomas Kragh
Budget: 3 780 000 SEK
The main purpose of this project is to further the understanding of exact Lagrangian manifolds in symplectic manifolds, and understand the relations to quantum physics. We propose the following specific goals:A) Apply Waldhausens K-theory to Fukaya categories to define and calculate higher K-invariants.B) Extent the notion of generating families of exact Lagrangians to a categorified version, which we call generating gerbes and which are defined for all embeddings, and hence defines new invariants of such.C) Compare with physics. There is already well-known connections between Lagrangians, generating families, and quantum physics. However, a direct relation with the deep connection between smooth structures and generating families seems unknown (unused). So, we especially want to elaborate on this connection and also generalize to the notion of generating gerbes from part B).D) Use part A) to calculate invariants defined in part B).Parts A) and B) are related to recent new development in the field (by Mohammed Abouzaid and I) and our current/previous work can be seen as small preliminary versions of what we hope to much more generally accomplish.