Relative Calabi-Yau structures
Christopher Brav, Tobias Dyckerhoff
TL;DR
This paper introduces relative noncommutative Calabi-Yau structures on functors of dg categories, providing a composition law that generalizes cobordism composition and applying it to topological Fukaya categories.
Contribution
It defines relative Calabi-Yau structures on dg functors and establishes a composition law, extending classical cobordism concepts to noncommutative geometry.
Findings
Established a composition law for Calabi-Yau cospans
Constructed Calabi-Yau structures on Fukaya categories
Generalized cobordism composition in noncommutative setting
Abstract
We introduce relative noncommutative Calabi-Yau structures defined on functors of differential graded categories. Examples arise in various contexts such as topology, algebraic geometry, and representation theory. Our main result is a composition law for Calabi-Yau cospans generalizing the classical composition of cobordisms of oriented manifolds. As an application, we construct Calabi-Yau structures on topological Fukaya categories of framed punctured Riemann surfaces.
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