Topological field theories associated with Calabi-Yau categories
Tristan Bozec, Damien Calaque, Sarah Scherotzke
TL;DR
This paper develops a framework for constructing higher categories of Calabi-Yau cospans, providing a noncommutative analog of Lagrangian correspondences, and relates it to topological field theories associated with Calabi-Yau categories.
Contribution
It introduces a functorial method to build symmetric monoidal higher categories of Calabi-Yau cospans and connects them to extended topological field theories.
Findings
Constructed symmetric monoidal higher categories of Calabi-Yau cospans.
Provided a functorial procedure for iterated nondegenerate cospans.
Factored the AKSZ extended TFT through Calabi-Yau cospans.
Abstract
We construct symmetric monoidal higher categories of iterated Calabi-Yau cospans, that are noncommutative analogs of iterated lagrangian correspondences. We actually give a general (and functorial) procedure that applies to iterated nondegenerate cospans on certain comma categories. This allows us to factor the AKSZ fully extended TFT associated with the moduli of objects of a Calabi-Yau category (taking values in iterated lagrangian correspondences) through a fully extended TFT taking values in iterated Calabi-Yau cospans.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory