On Fibrations and nilpotency - some remarks upon two articles by I. M. James.
On Kan extensions of cohomology theories and Serre classes of groups
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 quasidomination of compacta
On real flag manifolds with cup-length equal to its dimension
We prove that for any positive integers there exists a real flag manifold with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.
On the genus of free loop fibrations over -spaces.
On the genus of represenattion spheres.
On the homological category of 3-manifolds.
Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).
On the Lusternik-Schnirelmann category in the theory of shape
On the Lusternik-Schnirelmann Category of Lie Groups.
On the Lusternik-Schnirelmann Category of Lie Groups: II.
On two results of Singhof
For a compact connected semisimple Lie group we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of , respectively the 1-dimensional relative category of a maximal torus in . The techniques will be classical, but we shall also apply some basic results concerning the so-called -category (cf. [14]).
On Whitehead's inequality, .
Product type inequalities for the geometric category.
Quelques contre-exemples pour la LS catégorie d'une algèbre de cochaînes
À toute algèbre de cochaînes sont associés les invariants numériques suivants : , et qui approximent, pour tout corps et lorsque , la catégorie au sens de Lusternik-Schnirelmann de l’espace . Nous montrons dans cet article que ces trois invariants sont deux à deux distincts.
Rational category of the space of sections of a nilpotent bundle.
Remarks on minimal round functions
We describe the structure of minimal round functions on compact closed surfaces and three-dimensional manifolds. The minimal possible number of critical loops is determined and typical non-equisingular round function germs are interpreted in the spirit of isolated line singularities. We also discuss a version of Lusternik-Schnirelmann theory suitable for round functions.
Stability of Critical Points under Small Perturbations. Part I: Topological Theory.
Sur la catégorie de Lusternik-Schnirelmann des algèbres de cochaînes
Nous introduisons une nouvelle définition d’un invariant bicat pour une algèbre de cochaînes connexe et 1-connexe, de type fini sur un corps de caractéristique quelconque, et nous montrons d’une part, qu’il coïncide avec l’invariant cat introduit par S. Halperin et J.-M. Lemaire et d’autre part, qu’il est invariant par extension de corps et qu’il vérifie la conjecture de Ganéa.
Sur les invariants d'homotopie rationnelle liés à la L.S. catégorie.