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arXiv · 1004.0687

The Kapustin-Li formula revisited

Tobias Dyckerhoff·Daniel Murfet
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Abstract

We provide a new perspective on the Kapustin-Li formula for the duality pairing on the morphism complexes in the matrix factorization category of an isolated hypersurface singularity. In our context, the formula arises as an explicit description of a local duality isomorphism, obtained by using the basic perturbation lemma and Grothendieck residues. The non-degeneracy of the pairing becomes apparent in this setting. Further, we show that the pairing lifts to a Calabi-Yau structure on the matrix factorization category. This allows us to define topological quantum field theories with matrix factorizations as boundary conditions.

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Tobias Dyckerhoff, Daniel Murfet. 2010-04-05. The Kapustin-Li formula revisited. https://doi.org/10.1016/j.aim.2012.07.021

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