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## Banach Center Publications

1999 | 49 | 1 | 235-252
Tytuł artykułu

### Wecken theorems for Nielsen intersection theory

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EN
Abstrakty
EN
Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. Recently, the techniques of Nielsen theory have been applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), was introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular, it is a homotopy-invariant lower bound for the number of intersections of a pair of maps. The question of whether or not this lower bound is sharp can be thought of as the Wecken problem for intersection theory. In this paper, the Wecken problem for intersections is considered, and some Wecken theorems are proved.
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Rocznik
Tom
Numer
Strony
235-252
Opis fizyczny
Daty
wydano
1999
Twórcy
• Institute for Dynamics, Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A.
Bibliografia
• [1] R. Brooks and R. F. Brown, A lower bound for the Δ-Nielsen number, Trans. Amer. Math. Soc. 143 (1969), 555-564.
• [2] R. Brooks, The number of roots of f(x) = a, Bull. Amer. Math. Soc. 76 (1970), 1050-1052.
• [3] R. Brooks, On the sharpness of the $Δ_2$ and $Δ_1$ Nielsen numbers, J. Reine Angew. Math. 259 (1973), 101-108.
• [4] R. Dobreńko and Z. Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990), 1-14.
• [5] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85.
• [6] A. Fathi, F. Laudenbach et V. Poénaru, Travaux de Thurston sur les surfaces, Séminaire Orsay, Astérisque 66-67 (1979).
• [7] M. Hirsch, Differential Topology, Springer-Verlag, Berlin, 1976.
• [8] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, RI, 1983.
• [9] B. Jiang, Fixed points and braids, Invent. Math. 75 (1984), 69-74.
• [10] C. McCord, A Nielsen theory for intersection numbers, Fund. Math. 152 (1997), 117-150.
• [11] C. McCord, The three faces of Nielsen: comparing coincidence numbers, intersection numbers and root numbers, in preparation.
• [12] J. Milnor, Lectures on the h-Cobordism Theorem, Princeton Univ. Press, 1965.
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Bibliografia
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