On the negative cyclic homology of shc-algebras |
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Authors: | Bitjong Ndombol Mohammed El Haouari |
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Affiliation: | (1) Faculté des Sciences, Département de Mathématiques, Université de Dschang, BP 96 Dschang, Cameroun;(2) UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq, France |
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Abstract: | Let be a field of characteristic and S 1 the unit circle. We prove that the shc-structure on a cochain algebra (A,d A ) induces an associative product on the negative cyclic homology HC *− A. When the cochain algebra (A,d A ) is the algebra of normalized cochains of the simply connected topological space X with coefficients in , then HC *− A is isomorphic as a graded algebra to the S 1-equivariant cohomology algebra of LX, the free loop space of X. We use the notion of shc-formality introduced in Topology 41, 85–106 (2002) to compute the S 1-equivariant cohomology algebras of the free loop space of the complex projective space when n + 1 = 0 [p] and of the even spheres S 2n when p = 2. |
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Keywords: | Hochschild homology Cyclic homology Free loop space Borel fibration shc-algebra Algebra of divided powers S 1-equivariant cohomology |
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