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ATIYAH CLASS AND CHERN CHARACTER FOR GLOBAL MATRIX FACTORISATIONS

Part of: (Co)homology theory Homological algebra

Published online by Cambridge University Press:  08 January 2021

Bumsig Kim  and
Alexander Polishchuk Open the ORCID record for Alexander Polishchuk [Opens in a new window]
Bumsig Kim
Affiliation:
Korea Institute for Advanced Study
Alexander Polishchuk
Affiliation:
University of Oregon, Korea Institute for Advanced Study and National Research University Higher School of Economics, Russian Federation
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Abstract

We define the Atiyah class for global matrix factorisations and use it to give a formula for the categorical Chern character and the boundary-bulk map for matrix factorisations, generalising the formula in the local case obtained in [12]. Our approach is based on developing the Lie algebra analogies observed by Kapranov [7] and Markarian [9].

Keywords

matrix factorisationAtiyah classcategorical Chern characterboundary-bulk mapHochschild-Kostand-Rosenberg isomorphism

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions
Secondary: 18G60: Other (co)homology theories
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1445 - 1470
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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