Abstract
The aim of this paper is to generalize the Hochschild-Kostant-Rosenberg theorem to the case of singular varieties, more precisely, to manifolds with boundary and to varieties with isolated singularities. In these situations, we define suitable algebras of functions and study the localization of the corresponding Hochschild homology. The tool we use is the Teleman localization process. In the case of isolated singularities, the closed Hochschild homology corresponds to the intersection complex which relates the objects defined here to intersection homology.
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Brasselet, J.P., Legrand, A. Teleman localization of Hochschild homology in a singular setting. Russ. J. Math. Phys. 16, 391–403 (2009). https://doi.org/10.1134/S1061920809030078
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DOI: https://doi.org/10.1134/S1061920809030078