Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues

Abstract

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).