CYCLIC HOMOLOGY OF FORMAL SPACES

[摘要] Let X be a 1-connected topological space; we assume that X is Q-formal. We prove that the Connes operator S is zero on the reduced cyclic homology of X. Since there is an isomorphism between the cyclic homology and the equivariant homology of the free loop space, this result can be formulated as follows: Let X be a formal space, then the equivariant cohomology of the free loop space on X is the direct sum of H-* (BS1) and a graded H-* (BS1)-module T-* on which the structure of H-* (BS1)-module is trivial; moreover, the cohomology of the free loop space is the direct sum of T-* and T-*-1.

[发布日期] 1994-01-17