A suspension spectral sequence for vn-periodic homotopy groups.
Acyclic decomposition of acyclic spaces
Adams completion and Postnikov systems
Čech extensions and localization of homotopy functors
Cellular covers of cotorsion-free modules
In this paper we improve recent results dealing with cellular covers of R-modules. Cellular covers (sometimes called colocalizations) come up in the context of homotopical localization of topological spaces. They are related to idempotent cotriples, idempotent comonads or coreflectors in category theory. Recall that a homomorphism of R-modules π: G → H is called a cellular cover over H if π induces an isomorphism , where π⁎(φ) = πφ for each (where maps are acting on the left). On the one hand,...
Clones of spaces and maps in homotopy theory.
Cochains and homotopy type
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
Colocalizations and their realizations as spectra.
Completed representation ring spectra of nilpotent groups.
Completions of Z-Tate cohomology of periodic spectra.
Continuous Morava K-Theory and the Geometry of the In-Adic Tower.
Correction to "The Boolean algebra of spectra", Vol. 54 (1979), pp. 368-377.
Cosimplicial resolutions and homotopy spectral sequences in model categories.
Dans le fibré de l'espace des lacets libres, la fibre n'est pas, en général, totalement non cohomologue a zéro.
Definable orthogonality classes in accessible categories are small
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka’s principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class of morphisms in a locally presentable category of structures, the orthogonal class of objects is a small-orthogonality...
Elliptic spaces with the rational homotopy type of spheres.
Equivariant stable homotopy and Sullivan's conjecture.
Exploring W.G. Dwyer's tame homotopy theory.
Let Sr be the category of r-reduced simplicial sets, r ≥ 3; let Lr-1 be the category of (r-1)-reduced differential graded Lie algebras over Z. According to the fundamental work [3] of W.G. Dwyer both categories are endowed with closed model category structures such that the associated tame homotopy category of Sr is equivalent to the associated homotopy category of Lr-1. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology,...
Fake Lie groups and maximal tori. I.
Fake Lie groups and maximal tori. II.