The Brown-Peterson homology and nilpotence of the infinite special orthogonal group.
The chromatic -term for .
The cohomology algebra of certain free loop spaces
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 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 -term of the descent spectral sequence for continuous -spectra.
The E. H. P. Spectral Sequence.
The Fixed Point Transfer of Fibre-Preserving Maps.
The Hochschild cohomology ring of the singular cochain algebra of a space
We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra....
The homology and Morava K-theory of ..2SU(n).
The Homotopy Category of Spectra. III.
The Homotopy Category of Spectra.II.
The homotopy groups of the L2-localized Mahowald spectrum.
The Krull filtration on the category and cohomology of spaces. (La filtration de Krull de la categorie et la cohomologie des espaces.)
The level of real projective spaces.
The Morava -Theory Eilenberg-Moore spectral sequence.
The Salvetti complex and the little cubes
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...
The Structure of Morava Stabilizer Algebras.
The Transfer in Homological Algebra.
Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups.