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

Abstract

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 analogue 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.