A note on the transfer map.
Categorical length, relative L-S category and higher Hopf invariants
In this paper we introduce the categorical length, a homotopy version of Fox categorical sequence, and an extended version of relative L-S category which contains the classical notions of Berstein-Ganea and Fadell-Husseini. We then show that, for a space or a pair, the categorical length for categorical sequences is precisely the L-S category or the relative L-S category in the sense of Fadell-Husseini respectively. Higher Hopf invariants, cup length, module weights, and recent computations by Kono...
Co-H-grupos: Obstrucción a la commutatividad y aplicaciones centrales.
Double point self-intersection surfaces of immersions.
Freudenthal-Invariante.
Generalized Higher Order Cohomology Operations Induced by the Diagonal Mapping.
Geometric interpretations of the generalized Hopf invariant.
Geometric proof of the easy part of the Hopf invariant one theorem
Geometry of normed bilinear maps and the 16-square problem.
Gruppi di allacciamento : una generalizzazione funtoriale dell'invariante di Hopf
Link maps and the geometry of their invariants.
On Lusternik-Schnirelmann category of SO(10)
Let G be a compact connected Lie group and p: E → ΣA be a principal G-bundle with a characteristic map α: A → G, where A = ΣA₀ for some A₀. Let with F₀ = ∗, F₁ = ΣK₁ and Fₘ ≃ G be a cone-decomposition of G of length m and F’₁ = ΣK’₁ ⊂ F₁ with K’₁ ⊂ K₁ which satisfy up to homotopy for all i. Then cat(E) ≤ m + 1, under suitable conditions, which is used to determine cat(SO(10)). A similar result was obtained by Kono and the first author (2007) to determine cat(Spin(9)), but that result could not...
On Pierce-like idempotents and Hopf invariants.
On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.
The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This...
On the homotopy category of Moore spaces and the cohomology of the category of abelian groups
The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.
Opérations cohomologiques secondaires
Opérations cohomologiques secondaires (suite)
Quadruple points of 3-manifolds in S4.
Relationen für primäre Homotopieoperationen und eine verallgemeinerte EHP-Sequenz
Relations entre opérations cohomologiques secondaires