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
Two topological definitions of a Nielsen number for coincidences of noncompact maps.