Relative Calabi-Yau structures

被引：14
|
作者：
Brav, Christopher [1 ]
Dyckerhoff, Tobias [2 ]
机构：
[1] Natl Res Univ, Higher Sch Econ, Lab Mirror Symmetry, NRU HSE, 6 Usacheva Str, Moscow 119048, Russia
[2] Univ Hamburg, Fachbereich Math, Bundesstr 55, D-20146 Hamburg, Germany
来源：
COMPOSITIO MATHEMATICA | 2019年 / 155卷 / 02期
关键词：
differential graded categories; noncommutative Calabi-Yau structures; CYCLIC HOMOLOGY; CATEGORIES;
D O I：
10.1112/S0010437X19007024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：372 / 412
页数：41
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