Massey Products and H (p, q)-Systems.
Module derivations and cohomological splitting of adjoint bundles
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...
Morava K-theory of Double Loop Spaces of Spheres.
Natural factorizations and the Kan extension of cohomology theories
Noetherian loop spaces
The class of loop spaces of which the mod cohomology is Noetherian is much larger than the class of -compact groups (for which the mod cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space of such an object and prove it is as small as expected, that is, comparable to that of . We also show that X differs basically from the classifying space of a -compact group...
Obstruction Theory in Fiber Spaces.
On Convergence of Spectral Sequences.
On Kan extensions of cohomology theories and Serre classes of groups
On real-oriented Johnson-Wilson cohomology.
On -equivariant homology.
On the Adams spectral sequence for -modules.
On the cohomology of some Hopf algebroids and Hattori-Stong theorems.
On the cohomology ring of the free loop space of a wedge of spheres.
On the Convergence of the Adams Spectral Sequences.
On the Detection of Some Elements in the Image of the Double Transfer Using K(2)-Theory.
On the homology of mapping spaces
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
On the Hurewicz image of the cokernel J spectrum
On the mod p Betti numbers of loop spaces.
On the topological invariance of the basic cohomology.
On the Unstable Homotopy Spectral Sequences.