CONSTRUCTION OF MULTIPLY FIXED n-VALUED MAPS
نویسنده
چکیده
A self-map, either single-valued or multi-valued, is multiply fixed if every map homotopic to it has at least two fixed points. Let p : X̃ → X be a finite covering space, of degree n, of a connected finite polyhedron, and let f : X → X be a map. We lift f to an n-valued map φp,f : X̃ ( X̃ and prove that it is multiply fixed if the Nielsen number of f is greater than or equal to two. We obtain a formula for the Nielsen number of φp,f in terms of the Nielsen number of f , the induced fundamental group homomorphism of f , and the monodromy action of the covering space. We describe specific constructions of the n-valued maps φp,f on graphs, orientable double covers, handlebodies, free G-spaces and nilmanifolds. Subject Classification 55M20, 54C60, 57M10, 14H30, 22E25, 20E05,
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