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Tytuł artykułu
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Warianty tytułu
Języki publikacji
Abstrakty
In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_1(X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-18
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-02-26
poprawiono
1996-11-13
poprawiono
1997-09-18
poprawiono
1998-02-16
Twórcy
autor
- Università degli Studi di Milano, Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy, ferrario@vmimat.mat.unimi.it
Bibliografia
- [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971.
- [DHT] O. Davey, E. Hart and K. Trapp, Computation of Nielsen numbers for maps of closed surfaces, Trans. Amer. Math. Soc. 348 (1996), 3245-3266.
- [FaHu] E. Fadell and S. Husseini, The Nielsen number on surfaces, in: Contemp. Math. 21, Amer. Math. Soc., 1983, 59-98.
- [FeHi] A. Fel'shtyn and R. Hill, The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion, K-Theory 8 (1994), 367-393.
- [Ha] B. Halpern, Periodic points on the Klein bottle, manuscript.
- [He] P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), 267-289.
- [HKW] P. R. Heath, E. Keppelmann and P. N. S. Wong, Addition formulae for Nielsen numbers and Nielsen-type numbers of fibre preserving maps, Topology Appl. 67 (1995), 133-157.
- [Hu] S. Y. Husseini, Generalized Lefschetz numbers, Trans. Amer. Math. Soc. 272 (1982), 247-274.
- [J] B. J. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983.
- [MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Dover, 1966.
- [McC] C. K. McCord, Computing Nielsen numbers, in: Nielsen Theory and Dynamical Systems (South Hadley, Mass., 1992), Contemp. Math. 152, Amer. Math. Soc., Providence, 1993, 249-267.
- [W] P. Wong, Fixed-point theory for homogeneous spaces, Amer. J. Math. 120 (1998), 23-42.
- [Y] C. Y. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217-241.
Typ dokumentu
Bibliografia
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