The Classification of Simply Connected H-Spaces with Three Cells I.
The Cohomology of the Morava Stabilizer Algebras.
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 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 Exponential Law of Maps. II.
The Finiteness Obstructions for Nilpotent Spaces lie in D (...).
The first k-invariant, Quillen's space BG+ and the construction of Kann and Thurston.
The generalized Boardman homomorphisms
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b n: π n(X)→H n(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π n(X)→E n(X), F n(X)→(E∧F)n(X), F n(X)→H n(X;π 0 F) and F n(X)→H n+t(X;π t F) for other cohomology theories E *(−) and F *(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy...
The Gray filtration on phantom maps
This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set. If the condition...
The Group of Large Diffeomorphisms in General Relativity
We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
The Hatcher-Waldhausen map is a spectrum map.
The Homotype Type of a Combinatorially Aspherical Presentation.
The Krull filtration on the category and cohomology of spaces. (La filtration de Krull de la categorie et la cohomologie des espaces.)
The ...-Module Structure for the Cohomology of Two-Stage Spaces.
The ...(p) Cohomology of Some k Stage Postnikov Systems
The Primitive Elements in MU* K(Z/p, 1).
The Section Problem and the Lifting Problem.
The Smale invariant of a knot.
The ...-Spectrum for Brown-Peterson Cohomology. Part I
The vanishing of Steenrod squares on H-spaces.