Relative Calabi–Yau structures

2019/02/01 by Christopher Brav, Tobias Dyckerhoff · 11 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · doi:10.1112/s0010437x19007024

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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