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RiemannRoch Theorems via Deformation Quantization
, 1997
"... Abstract. We deduce the RiemannRoch type formula expressing the microlocal Euler class of a perfect complex of Dmodules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the RiemannRoch type theorem for periodic cyclic cocycles of a symplecti ..."
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Cited by 37 (9 self)
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Abstract. We deduce the RiemannRoch type formula expressing the microlocal Euler class of a perfect complex of Dmodules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the RiemannRoch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper. 1.
ON THE COHOMOLOGY RING OF AN ALGEBRA
, 1998
"... We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum multiplication on Floer cohomology of free loop spaces. We discus ..."
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Cited by 22 (9 self)
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We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum multiplication on Floer cohomology of free loop spaces. We discuss some examples, as well as applications to index theorems, characteristic classes and deformations.