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Module derivations and cohomological splitting of adjoint bundles

Akira Kono, Katsuhiko Kuribayashi (2003)

Fundamenta Mathematicae

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...

Modulo C homotopy

J. R. Dennett (1982)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Motivic functors.

Dundas, Bjørn Ian, Röndigs, Oliver, Østvær, Paul Arne (2003)

Documenta Mathematica

Multifibrations. A class of shape fibrations with the path lifting property

Antonio Giraldo, José M. R. Sanjurjo (2001)

Czechoslovak Mathematical Journal

In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration. Multifibrations have the interesting property of being characterized in a completely intrinsic way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations (and also, with some restrictions,...

Multiplicative maps from Hℤ to a ring spectrum R-a naive version

Stanisław Betley (2012)

Fundamenta Mathematicae

The paper is devoted to the study of the space of multiplicative maps from the Eilenberg-MacLane spectrum Hℤ to an arbitrary ring spectrum R. We try to generalize the approach of Schwede [Geom. Topol. 8 (2004)], where the case of a very special R was studied. In particular we propose a definition of a formal group law in any ring spectrum, which might be of independent interest.

Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

Michael Slack (1999)

Fundamenta Mathematicae

A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem...

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