The free loop space equivariant cohomology algebra of some formal spaces. (English) Zbl 1203.57014
Authors’ abstract: Let \({\mathbb{K}}\) be a field of characteristic \(p > 0\) and \(S ^{1}\) the unit circle. We construct a model for the negative cylic homology of a commutative cochain algebra with two stages Sullivan minimal model. Using the notion of \(shc\)-formality introduced in B. Ndombol and J.-C. Thomas [Topology 41, No. 1, 85–106 (2002; Zbl 1011.16008)], the main result of B. Ndombol and M. El Haouari [Math. Ann. 338, No. 2, 385–403 (2007; Zbl 1136.57018)] and techniques of M. Vigué-Poirrier [J. Pure Appl. Algebra 91, No. 1–3, 347–354 (1994; Zbl 0802.55011)] we compute the \(S^{1}\)-equivariant cohomology algebras of the free loop spaces of the infinite complex projective space \({\mathbb{CP}(\infty)}\) and the odd spheres \(S^{2q+1}\).
Reviewer: Jean Claude Thomas (Angers)
MSC:
| 57T30 | Bar and cobar constructions |
Keywords:
Hochschild homology; cyclic homology; free loop space; Borel space; \(shc\)-algebra; equivariant cohomologyReferences:
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