Relative Calabi-Yau structures

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.

36 pages, preliminary version, comments welcome

References in corpus (5)

• Higher Topos Theory
• On the Classification of Topological Field Theories
• Mirror symmetry: from categories to curve counts
• Calabi-Yau structures on topological Fukaya categories
• A1-homotopy invariants of topological Fukaya categories of surfaces

Cited by in corpus (27)

• Pre-Calabi-Yau algebras and double Poisson brackets
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Orlov and Viterbo functors in partially wrapped Fukaya categories
• Dimensional reduction in cohomological Donaldson-Thomas theory
• Pre-Calabi-Yau structures and moduli of representations
• Relative Calabi-Yau completions
• Gopakumar-Vafa invariants via vanishing cycles
• Odd sphere bundles, symplectic manifolds, and their intersection theory
• Relative critical loci and quiver moduli
• Purity and 2-Calabi-Yau categories
• Calabi-Yau structures for multiplicative preprojective algebras
• Continuous and coherent actions on wrapped Fukaya categories
• Ginzburg algebras of triangulated surfaces and perverse schobers
• Global critical chart for local Calabi-Yau threefolds
• An ${\mathsf{A}}_{\infty }$ version of the Poincaré lemma
• Donaldson-Thomas invariants of length 2 flops
• The colimit of an $\infty$-local system as a twisted tensor product
• Shifted bisymplectic and double Poisson structures on non-commutative derived prestacks
• Singular chains on Lie groups and the Cartan relations II
• Calabi-Yau structures on (quasi-)bisymplectic algebras
• AS-regular algebras from acyclic spherical helices
• Singular Legendrian unknot links and relative Ginzburg algebras
• Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology
• Rational singularities for moment maps of totally negative quivers
• Persistence of unknottedness of clean Lagrangian intersections
• Derived equivalences of upper-triangular ring spectra via lax limits
• Categorical non-properness in wrapped Floer theory