On the real cohomology of spaces of free loops on manifolds
Tom 150 / 1996
Fundamenta Mathematicae 150 (1996), 173-188
DOI: 10.4064/fm-150-2-173-188
Streszczenie
Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen's iterated integral map. Let $\mathbb{T}$ be the circle group. The $\mathbb{T}$-equivariant cohomology of LX is also studied in terms of the cyclic homology of Ω(X).
