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A relative Nielsen number
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Nielsen root theory and Hopf degree theory
The Nielsen root number N(f ; c) of a map f : M → N at a point c ∈ N is a homotopy invariant lower bound for the number of roots at c, that is, for the cardinality of f−1(c). There is a formula forExpand
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On the location of fixed points on pairs of spaces
Let f: (X, A)→(X, A) be an admissible selfmap of a pair of metrizable ANR's. A Nielsen number of the complement N(f; X, A) and a Nielsen number of the boundary n(f; X, A) are defined. N(f; X, A) is aExpand
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Fixed point sets in a prescribed homotopy class
Abstract Let ⨍:X→X be a self-map of a compact ANR and A ⊂ X a closed subset. Two conditions are stated which are necessary for the realization of A as the fixed point set of a map g in the homotopyExpand
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Nielsen numbers for maps of triads
Abstract Let ƒ:(X,A1,A2) → (X,A1,A2) be a selfmap of a triad which consist of a compact connected polyhedron X and two subpolyhedra A1 and A2 so that X = A1 ∪ A2. A Nielsen type number N(ƒ;A1 ∪ A2),Expand
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Nielsen theory of roots of maps of pairs
Abstract A relative root Nielsen number N rel (ƒ; c) is introduced which is a homotopy invariant lower bound for the number of roots at c for a map of pairs of spaces ƒ : (X, A) → (Y, B) and c ϵ Y .Expand
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The absolute degree and the Nielsen root number of compositions and Cartesian products of maps
Abstract Brouwer's homological degree has the multiplicative property for the composition of maps. That is, if f :X→Y and g :Y→Z are maps between closed oriented manifolds X,Y,Z of the sameExpand
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