Nielsen numbers and Lefschetz numbers on solvmanifolds
نویسندگان
چکیده
منابع مشابه
Lefschetz and Nielsen Coincidence Numbers on Nilmanifolds and Solvmanifolds
Suppose M 1 ; M 2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps f,g:M 1 ?! M 2 , the Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are measures of the number of coincidences of f and g: points x 2 M 1 with f(x) = g(x). A manifold is a nilmanifold (solvmanifold) if it is a homogeneous space of a nilpotent (solvable) ...
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In 10], it was claimed that Nielsen coincidence numbers and Lefschetz coincidence numbers are related by the inequality N (f; g) jL(f; g)j for all maps f; g : S 1 ! S 2 between compact orientable solvmanifolds of the same dimension. It was further claimed that N (f; g) = jL(f; g)j when S 2 is a nilmanifold. A mistake in that paper has been discovered. In this paper, that mistake is partially re...
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A well-known lower bound for the number of xed points of a self-map f : X ?! X is the Nielsen number N(f). Unfortunately, the Nielsen number is diicult to calculate. The Lefschetz number L(f), on the other hand, is readily computable, but does not give a lower bound for the number of xed points. In this paper, we investigate conditions on the space X which guarantee either N(f) = jL(f)j or N(f)...
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Suppose X , Y are manifolds, f ,g : X → Y are maps. The well-known coincidence problem studies the coincidence set C = {x : f (x) = g(x)}. The number m= dimX −dimY is called the codimension of the problem. More general is the preimage problem. For a map f : X → Z and a submanifold Y of Z, it studies the preimage set C = {x : f (x) ∈ Y}, and the codimension is m = dimX + dimY − dimZ. In case of ...
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A simple argument is given as to why it is always trivial to calculate Lefschetz and Nielsen numbers for iterated function systems or dynamical systems in hyperspaces. The problem is reduced to a simple combinatorical situation on a finite set. In the papers [3], [4] the question was raised whether the Lefschetz or even the Nielsen number might be used in the hyperspace H(X) of all nonempty com...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.147.153