One codimensional Wecken type theorems.
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.
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 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 Nielsen product formula for coincidences
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.
Weak Wecken's theorem for periodic points in dimension 3
We prove that a self-map f: M → M of a compact PL-manifold of dimension ≥ 3 is homotopic to a map with no periodic points of period n iff the Nielsen numbers for k dividing n all vanish. This generalizes the result from [Je] to dimension 3.
Lefschetz coincidence formula on non-orientable manifolds
We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.
Minimal number of periodic points for smooth self-maps of S³
Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate for all self-maps of S³.
Nielsen number of a covering map.
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