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Relative Calabi-Yau structures

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arxiv 1606.00619 v1 pith:WW7ERFWH submitted 2016-06-02 math.AG math.ATmath.RT

Relative Calabi-Yau structures

Christopher Brav , Tobias Dyckerhoff This is my paper
classification math.AG math.ATmath.RT
keywords calabi-yaustructurescategoriescompositionrelativealgebraicapplicationarise
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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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