L-homology theory of FSQL-manifolds and the degree of FSQL-mappings
A homology theory of Banach manifolds of a special form, called FSQL-manifolds, is developed, and also a homological degree of FSQL-mappings between FSQL-manifolds is introduced.
Linking and coincidence invariants
Given a link map f into a manifold of the form Q = N × ℝ, when can it be deformed to an “unlinked” position (in some sense, e.g. where its components map to disjoint ℝ-levels)? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions , ε = + or ε = -, which often answer this question completely and which, in addition, turn out to distinguish a great number of different link homotopy classes. In certain cases they even allow a complete...
Linking pairings on singular spaces.
Local cohomological properties of homogeneous ANR compacta
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...
Local constribution to the Lefschetz fixes point formula.
Localisation of Unstable Ap-Algebras and Smith Theory.
Locally admissible multi-valued maps
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
LS category of classifying spaces and 2-cones.
LS-catégorie de CW-complexes à 3 cellules en théorie homototique R-locale.
We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S2n Uk[i2n,i2n] e4n. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.
LS-category of classifying spaces.
LS-category of classifying spaces. II.
Lusternik-Schnirelmann category: a geometric approach
Lusternik-Schnirelmann category and minimal coverings with contractible sets.
Lusternik-Schnirelmann Category and the Moore Spectral Sequence.
Lusternik-Schnirelmann-categorical sections
M. M. Postnikov: his life, work and legacy
Mapping theorems for compacta with an arbitrary involution
Mappings with 1-dimensional absolute neighborhood retract fibers
Maps into the torus and minimal coincidence sets for homotopies
Let X,Y be manifolds of the same dimension. Given continuous mappings , i = 0,1, we consider the 1-parameter coincidence problem of finding homotopies , 0 ≤ t ≤ 1, such that the number of coincidence points for the pair is independent of t. When Y is the torus and f₀,g₀ are coincidence free we produce coincidence free pairs f₁,g₁ such that no homotopy joining them is coincidence free at each level. When X is also the torus we characterize the solution of the problem in terms of the Lefschetz...
Maximal elements and equilibria of generalized games for -majorized and condensing correspondences.