A Cech-Hurewicz Isomorphism Theorem for Movable Metric Compacta.
A classification of cohomology transfers for ramified covering maps
We construct a cohomology transfer for n-fold ramified covering maps. Then we define a very general concept of transfer for ramified covering maps and prove a classification theorem for such transfers. This generalizes Roush's classification of transfers for n-fold ordinary covering maps. We characterize those representable cofunctors which admit a family of transfers for ramified covering maps that have two naturality properties, as well as normalization and stability. This is analogous to Roush's...
A classification of secondary cohomology operations
A Coclassifying Map for the Inclusion of the Wedge in the Product.
A combinatorial interpretation of homotopy groups of polyhedra
A conjecture on the unstable Adams spectral sequences for SO and U
We give a systematic account of a conjecture suggested by Mark Mahowald on the unstable Adams spectral sequences for the groups SO and U. The conjecture is related to a conjecture of Bousfield on a splitting of the E₂-term and to an algebraic spectral sequence constructed by Bousfield and Davis. We construct and realize topologically a chain complex which is conjectured to contain in its differential the structure of the unstable Adams spectral sequence for SO. A filtration of this chain complex...
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A Drived Homotopy Product.
A geometric decomposition of spaces into cells of different types.
A higher dimensional homotopy sequence.
A homotopy 2-groupoid from a fibration.
A homotopy double groupoid of a Hausdorff space.
A homotopy double groupoid of a Hausdorff space. II: A van Kampen theorem.
A new invariant and parametric connected sum of embeddings
We define an isotopy invariant of embeddings of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...
A note on generalized equivariant homotopy groups
In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce Γ-Rhodes groups, where Γ admits a certain co-grouplike structure. Evaluation subgroups of Γ-Rhodes groups are discussed.
A note on the transfer map.
A product involving the -family in stable homotopy theory.
A propos de conjectures de Serre et Sullivan.
A Relation Between Equivariant and Non-equivariant Stable Cohomotopy.
A Semigroup of Simple Homotopy Types.