Formality of Cyclic Chains
نویسنده
چکیده
We prove a conjecture raised by Tsygan [12], namely the existence of an L∞-quasiisomorphism of L∞-modules between the cyclic chain complex of smooth functions on a manifold and the differential forms on that manifold. Concretely, we prove that the obvious u-linear extension of Shoikhet’s morphism of Hochschild chains solves Tsygan’s conjecture.
منابع مشابه
L∞-morphisms of Cyclic Chains
Recently the first two authors [1] constructed an L∞-morphism using the S1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors [5], [9].
متن کاملOn L∞-morphisms of Cyclic Chains
Recently the first two authors [1] constructed an L∞-morphism using the S1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors [5], [10].
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We conjecture an explicit formula for a cyclic analog of the Formality L∞-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To prove it we construct a cohomological version of the Connes-Tsygan bicomplex in cyclic homology. As an application of the cyclic Formality conjecture, we ...
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