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
The obstruction to the deformation of a map out of a subspace [Book]
The Reidemeister trace and the calculation of the Nielsen number
The relative coincidence Nielsen number
We define a relative coincidence Nielsen number for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing by the ordinary Nielsen numbers.
The semi-index product formula
We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and .
The solution of a Fučík's conjecture
The twisted products of spheres that have the fixed point property
By a twisted product of Sⁿ we mean a closed, 1-connected 2n-manifold M whose integral cohomology ring is isomorphic to that of Sⁿ × Sⁿ, n ≥ 3. We list all such spaces that have the fixed point property.
The universal functorial Lefschetz invariant
We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and -torsion of mapping tori. We examine its behaviour under fibrations.
The Wecken property of the projective plane
A proof is given of the fact that the real projective plane has the Wecken property, i.e. for every selfmap , the minimum number of fixed points among all selfmaps homotopic to f is equal to the Nielsen number N(f) of f.
Theorem on signatures
Topological and approximation methods of degree theory of set-valued maps [Book]
Topological contraction principle
Topological degree and Sperner's lemma
Topological essentiality for multivalued weighted mappings
Transfer maps for fibrations and duality