Nielsen coincidence numbers, Hopf invariants and spherical space forms
نویسندگان
چکیده
منابع مشابه
Nonstabilized Nielsen coincidence invariants and Hopf--Ganea homomorphisms
In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory as our main tool. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coinciden...
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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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We give a simplified proof of J. A. Wolf’s classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some non-obvious redundancy. The groups are the same as the Frobenius complements of finite group theory. In chapters 4–7 of his famous Spaces of Constant Curvature [7], J. A. Wolf classified the ...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2014
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2014.14.1541