The cohomology ring of free loop spaces.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
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 coincidence Nielsen number for maps into real projective spaces
We give an algorithm to compute the coincidence Nielsen number N(f,g), introduced in [DJ], for pairs of maps into real projective spaces.
The compact extension property: the role of compactness
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 ’s.
The complex of words and Nakaoka stability.
The complex oriented cohomology of extended powers
We examine the behaviour of a complex oriented cohomology theory on , the -extended power of a space , seeking a description of in terms of the cohomology . We give descriptions for the particular cases of Morava -theory for any space and for complex cobordism , the Brown-Peterson theories BP and any Landweber exact theory for a wide class of spaces.
The compression theorem III: Applications.
The computation of Stiefel-Whitney classes
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
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.
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
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.
The cyclic groups and the free loop space.
The cyclic homology of p-adic reductive groups.
The cyclic homology of the group rings.
The cyclotomic trace and algebraic K-theory of spaces.
The de Rham theorem for the noncommutative complex of Cenkl and Porter.
The Degree of a Map Between Surfaces.
The degrees of certain strata of the dual variety
The dilatation invariant in the homotopy of spheres.
The d-invariant of compact nilmanifolds.