Tetrahedra on deformed spheres and integral group cohomology.
The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group.
The boundary-Wecken classification of surfaces.
The Brouwer Fixed Point Theorem for Some Set Mappings
For some classes of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.
The Brouwer-Jordan theorem
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
The coincidence Nielsen number for maps into real projective spaces
We give an algorithm to compute the coincidence Nielsen number N(f,g), introduced in [DJ], for pairs of maps into real projective spaces.
The Fixed Point Index of Fibre-Preserving Maps.
The Fixed Point Transfer of Fibre-Preserving Maps.
The Idzik type quasivariational inequalities and noncompact optimization problems
The index of discontinuous vector fields.
The least number of fixed points of bimaps
The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces
The Lefschetz fixed point theorem for some noncompact multi-valued maps
The Lefschetz-Hopf theorem and axioms for the Lefschetz number.
The Leray-Schauder index and the fixed point theory for arbitrary ANRs
The minimizing of the Nielsen root classes
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen...
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
The Nielsen coincidence theory on topological manifolds
We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
The Nielsen product formula for coincidences