Relative Calabi-Yau structures

被引：18

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.

引用

页码：372 / 412

页数：41

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