Wyniki wyszukiwania

1

On the real cohomology of spaces of free loops on manifolds

100%

Kuribayashi K.

Fundamenta Mathematicae

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1996

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tom 150

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nr 2

173-188

EN

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).

2

Module derivations and cohomological splitting of adjoint bundles

63%

Kono A., Kuribayashi K.

Fundamenta Mathematicae

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2003

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tom 180

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nr 3

199-221

EN

Let G be a finite loop space such that the mod p cohomology of the classifying space BG is a polynomial algebra. We consider when the adjoint bundle associated with a G-bundle over M splits on mod p cohomology as an algebra. In the case p = 2, an obstruction for the adjoint bundle to admit such a splitting is found in the Hochschild homology concerning the mod 2 cohomologies of BG and M via a module derivation. Moreover the derivation tells us that the splitting is not compatible with the Steenrod operations in general. As a consequence, we can show that the isomorphism class of an SU(n)-adjoint bundle over a 4-dimensional CW complex coincides with the homotopy equivalence class of the bundle.

3

The cohomology algebra of certain free loop spaces

63%

Yamaguchi T., Kuribayashi K.

Fundamenta Mathematicae

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1997

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tom 154

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nr 1

57-73

EN

Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of the Hochschild homology of a graded complete intersection algebra over a field.

Ograniczanie wyników

3 Fundamenta Mathematicae

3 Kuribayashi K.

1 Kono A.

1 Yamaguchi T.

1 2003

1 1997

1 1996

On the real cohomology of spaces of free loops on manifolds

Module derivations and cohomological splitting of adjoint bundles

The cohomology algebra of certain free loop spaces