Smith theory and the functor T.
Smith theory for algebraic varieties.
Solvability Of Operator Equations And Periodic Solutions Of Semilinear Hyperbolic Equations
Solving Systems of Polynomial Equations by Bounded and Real Homotopy.
Some applications of Coincidence theory.
Some applications of the topological degree theory to multi-valued boundary value problems [Book]
Some combinatorial results about the operators with jumping nonlinearities
Some elementary applications of topological degree.
Some extension and classification theorems for maps of movable spaces
Some homotopy theoretical questions arising in Nielsen coincidence theory
Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.
Some new results on composition of quadratic forms.
Some Results on Maps That Factor through a Tree
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...
Spaces with fibered approximation property in dimension n
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: m × n → M there exists a map g′: m × n → M such that g′ is ɛ-homotopic to g and dim g′ (z × n) ≤ n for all z ∈ m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].
Spherical maps
Stability of Critical Points under Small Perturbations. Part I: Topological Theory.
Steenrod's Equivariant Moore Space Problem for Cohomologically Trivial Modules.
Strong Cohomological Dimension
We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that if X is a separable metric ANR and G is a countable Abelian group. Hence for any separable metric ANR X.
Strong surjectivity of mappings of some 3-complexes into 3-manifolds
Let K be a CW-complex of dimension 3 such that H³(K;ℤ) = 0, and M a closed manifold of dimension 3 with a base point a ∈ M. We study the problem of existence of a map f: K → M which is strongly surjective, i.e. such that MR[f,a] ≠ 0. In particular if M = S¹ × S² we show that there is no f: K → S¹ × S² which is strongly surjective. On the other hand, for M the non-orientable S¹-bundle over S² there exists a complex K and f: K → M such that MR[f,a] ≠ 0.
Strong surjectivity of mappings of some 3-complexes into
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min(g −1(a))|g ∈ [f] ≠ 0.
Strong surjectivity of maps from 2-complexes into the 2-sphere
Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = (f) has an integer solution, here (f)is the so-called vector-degree of f