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Cohomology of some graded differential algebras

Wojciech Andrzejewski, Aleksiej Tralle (1994)

Fundamenta Mathematicae

We study cohomology algebras of graded differential algebras which are models for Hochschild homology of some classes of topological spaces (e.g. homogeneous spaces of compact Lie groups). Explicit formulae are obtained. Some applications to cyclic homology are given.

On the real cohomology of spaces of free loops on manifolds

Katsuhiko Kuribayashi (1996)

Fundamenta Mathematicae

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 𝕋 be the circle group. The 𝕋 -equivariant cohomology...

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