منابع مشابه
Formality of Cyclic Chains
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.
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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 ...
متن کاملCochains and Homotopy Type
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
متن کاملTwisted Cochains and Higher Torsion
This paper gives a short summary of the central role played by Ed Brown’s “twisted cochains” in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisted cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR torsi...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.04.032