Formality of Cyclic Cochains
نویسنده
چکیده
We prove Kontsevich’s cyclic formality conjecture.
منابع مشابه
On the cyclic Formality conjecture
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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We introduce two coloured operads in sets – the lattice path operad and a cyclic extension of it – closely related to iterated loop spaces and to universal operations on cochains. As main application we present a formal construction of an E2-action (resp. framed E2-action) on the Hochschild cochain complex of an associative (resp. symmetric Frobenius) algebra.
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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].
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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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