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Relative Calabi–Yau structures

Part of: Abelian categories

Published online by Cambridge University Press:  12 February 2019

Christopher Brav  and
Tobias Dyckerhoff Open the ORCID record for Tobias Dyckerhoff [Opens in a new window]
Christopher Brav
Affiliation:
National Research University Higher School of Economics, Russian Federation, Laboratory of Mirror Symmetry, NRU HSE, 6 Usacheva str., Moscow, 119048, Russia email [email protected]
Tobias Dyckerhoff
Affiliation:
Fachbereich Mathematik, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany email [email protected]
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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.

Keywords

differential graded categoriesnoncommutative Calabi–Yau structures

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 2 , February 2019 , pp. 372 - 412
Copyright
© The Authors 2019 

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