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) ...
متن کاملLefschetz and Nielsen Coincidence Numbers on Nilmanifolds and Solvmanifolds, Ii
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...
متن کاملMethods in Nielsen Coincidence Theory
In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coincidence sets of those pairs of maps which are homotopic to (...
متن کاملHigher-order Nielsen Numbers
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 ...
متن کاملEquivariant Nielsen Invariants for Discrete Groups
For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f : X → X. Under mild hypotheses, these lower bounds are sharp. We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2003
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(02)00130-x