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1997 | 152 | 2 | 117-150
Tytuł artykułu

A Nielsen theory for intersection numbers

Treść / Zawartość
Warianty tytułu
Języki publikacji
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. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular, NI(f,g) gives a lower bound for the number of points of intersection for all maps homotopic to f and g.
Słowa kluczowe
Rocznik
Tom
152
Numer
2
Strony
117-150
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-01-18
poprawiono
1996-05-28
Twórcy
  • Institute for Dynamics, Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A., chris.mccord@uc.edu
Bibliografia
  • [1] R. Brooks, 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 removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy, Pacific J. Math. 39 (1971), 45-52.
  • [4] R. Dobreńko and Z. Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990), 1-14.
  • [5] A. Dold, Lectures on Algebraic Topology, Springer, Berlin, 1970.
  • [6] P. Heath, E. Keppelmann and P. Wong, Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps, Topology Appl. 67 (1995), 133-157.
  • [7] M. Hirsch, Differential Topology, Springer, Berlin, 1976.
  • [8] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, R.I., 1983.
  • [9] C. McCord, Estimating Nielsen numbers on infrasolvmanifolds, Pacific J. Math. 154 (1992), 345-368.
  • [10] C. McCord, The three faces of Nielsen: comparing coincidence numbers, intersection numbers and root numbers, in preparation.
  • [11] J. Milnor, Lectures on the h-Cobordism Theorem, Princeton Univ. Press, 1965.
  • [12] C.-Y. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217-241.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i2p117bwm
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