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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...

On the suspension homomorphism

S. Dragotti, G. Magro, L. Parlato (2002)

Bollettino dell'Unione Matematica Italiana

In this paper we investigate the conditions for the suspension homomorphism s : Θ r - 1 F S n - 1 , x 0 Θ r F S n , x 0 is onto or an isomorphism.

On weak i -homotopy equivalences of modules

Zheng-Xu He (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si definisce il gruppo di i —omotopia di un singolo modulo e si introduce la nozione di equivalenza i -omotopica debole. Sotto determinate condizioni per l'anello di base Λ oppure per i moduli considerati, le equivalenze i -omotopiche deboli coincidono con le equivalenze i -omotopiche (forti).

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