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- Title
On the negative cyclic homology of <i>shc</i> -algebras.
- Authors
Bitjong Ndombol; Mohammed Haouari
- Abstract
Abstract  Let $${\mathbb{K}}$$ be a field of characteristic $${p\geq 0}$$ 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 *â A. When the cochain algebra (A,d A ) is the algebra of normalized cochains of the simply connected topological space X with coefficients in $${\mathbb{K}}$$ , then HC *â A is isomorphic as a graded algebra to $${H^{-*}_{S^1}(LX;\mathbb{K})}$$ 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, 85â106 (2002) to compute the S 1-equivariant cohomology algebras of the free loop space of the complex projective space $${\mathbb{C}P(n)}$$ when n  1 = 0 [p] and of the even spheres S 2n when p = 2.
- Subjects
MATHEMATICAL analysis; MATHEMATICS; HOMOTOPY theory; GEOMETRY
- Publication
Mathematische Annalen, 2007, Vol 338, Issue 2, p385
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-006-0079-6