Relative Calabi–Yau structures

By Christopher Brav, Tobias Dyckerhoff. Compositio Mathematica, 2016

69 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e68540767565e2de1853132bba8a07b75cd3a96

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In Geometry and Topology

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Frederick J. Bourgeois III
7. Mark McLean
8. A. Oancea

In Mathematical Physics

1. P. Seidel
2. D. Auroux
3. M. Abouzaid
4. I. Smith
5. Alexander F. Ritter
6. Mark McLean
7. A. Oancea
8. Frederick J. Bourgeois III

Citations in the corpus

• Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, methodology): “n on the noncommutative divisor. Indeed, this was the denition of noncommutative divisor used in [34, Section 2f] (and which, under a dierent name, already appears in [31]; for related notions, see [19, 6]). Remark 2.1. Let’s suppose that Ris a eld of characteristic zero. One can then view the class”