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The cohomology algebra of certain free loop spaces

Toshihiro Yamaguchi, Katsuhiko Kuribayashi (1997)

Fundamenta Mathematicae

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 cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category

J. Bryden, P. Zvengrowski (1998)

Banach Center Publications

This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.

The coincidence index for fundamentally contractible multivalued maps with nonconvex values

Dorota Gabor (2000)

Annales Polonici Mathematici

We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.

The compact extension property: the role of compactness

Jos Bijl, Jan van Mill (1991)

Commentationes Mathematicae Universitatis Carolinae

We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for ANR ’s.

The complex oriented cohomology of extended powers

John Robert Hunton (1998)

Annales de l'institut Fourier

We examine the behaviour of a complex oriented cohomology theory G * ( - ) on D p ( X ) , the C p -extended power of a space X , seeking a description of G * ( D p ( X ) ) in terms of the cohomology G * ( X ) . We give descriptions for the particular cases of Morava K -theory K ( n ) for any space X and for complex cobordism M U , the Brown-Peterson theories BP and any Landweber exact theory for a wide class of spaces.

The computation of Stiefel-Whitney classes

Pierre Guillot (2010)

Annales de l’institut Fourier

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...

The Conley index for flows preserving generalized symmetries

Artur Pruszko (1999)

Banach Center Publications

Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.

The connective K-theory of spinor groups.

Luísa Magalhâes (1990)

Publicacions Matemàtiques

We study the properties of the connective K-theory with Z2 coefficients of the Lie groups Spin(n). This generalises some work by L. Hodgkin.

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

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