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Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations

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arxiv 1002.2116 v3 pith:3RI637MB submitted 2010-02-10 math.AG math.AC

Alexander Polishchuk , Arkady Vaintrob This is my paper · ORCID
classification math.AGmath.AC
keywords factorizationsmatrixcategorychernformulahirzebruch-riemann-rochanalogbilinear
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We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit expressions for the Chern character and the boundary-bulk maps and derive an analog of the Hirzebruch-Riemann-Roch formula for the Euler characteristic of the Hom-space between a pair of matrix factorizations. We also establish G-equivariant versions of these results.

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Cited by 1 Pith paper

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  1. Iterated traces in 2-categories and Lefschetz theorems

    math.AT 2019-08 conditional novelty 7.0 of 10

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.

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