On a class of multi-valued vector fields in Banach spaces
On a class of spaces for which the fixed-point property is characterized by homology groups
On a coincidence of mappings of compact spaces in topological groups
On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces.
On a nonlocal metric regularity of nonlinear operators
On a stability theorem for the fixed-point property
On cat(X).
On cohomological dimension of a space and its Stone-Čech compactification
On construction of signature of quadratic forms on infinite-dimensional abstract spaces.
On dimensionally restricted maps
Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an -subset of X such that and the restriction is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about...
On equivariant deformations of maps.
We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f|A fixpointfree, where A is a closed invariant submanifold of X with codim A ≥ 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed point free map if and only if the...
On Fibrations and nilpotency - some remarks upon two articles by I. M. James.
On finite groups acting on acyclic complexes of dimension two.
We conjecture that every finite group G acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where G is solvable, and under this additional hypothesis, the result holds for X acyclic.
On Fixed Points of Symplectic Maps.
On generalizing the Nielsen coincidence theory to non-oriented manifolds
We give an outline of the Nielsen coincidence theory emphasizing differences between the oriented and non-oriented cases.
On -bubbles in n-dimensional compacta
A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum...
On homotopically regular mappings of manifolds
On increment of the tangent argument along a curve
On Kan extensions of cohomology theories and Serre classes of groups
On locally simply connected toposes and their fundamental groups