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1991-1992 | 140 | 2 | 191-196
Tytuł artykułu

On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
Słowa kluczowe
Rocznik
Tom
140
Numer
2
Strony
191-196
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-07-24
poprawiono
1991-10-08
Twórcy
autor
  • Department of Mathematics, Bates College Lewiston, Maine 04240, U.S.A.
Bibliografia
  • [1] R. Brooks, Certain subgroups of the fundamental group and the number of roots of f(x)=a, Amer. J. Math. 95 (1973), 720-728.
  • [2] R. Brooks and R. Brown, A lower bound for the Δ-Nielsen number, Trans. Amer. Math. Soc. 143 (1969), 555-564.
  • [3] R. Brooks and P. Wong, On changing fixed points and coincidences to roots, Proc. Amer. Math. Soc., to appear.
  • [4] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott & Foresman, Glenview, Ill., 1971.
  • [5] A. Dold, Lectures on Algebraic Topology, Springer, Berlin 1972.
  • [6] E. Fadell and S. Husseini, Local fixed point index theory for non simply connected manifolds, Illinois J. Math. 25 (1981), 673-699.
  • [7] J. Jezierski, The Nielsen number product formula for coincidences, Fund. Math. 134 (1989), 183-212.
  • [8] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., 1982.
  • [9] T. Kiang, The Theory of Fixed Point Classes, Springer, Berlin 1989.
  • [10] C. McCord, Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds, Topology Appl., to appear.
  • [11] H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39.
  • [12] J. Vick, Homology Theory, Academic Press, New York 1973.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv140i2p191bwm
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