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1999 | 49 | 1 | 19-27
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Nielsen fixed point theory on manifolds

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The study of fixed points of continuous self-maps of compact manifolds involves geometric topology in a significant way in topological fixed point theory. This survey will discuss some of the questions that have arisen in this study and indicate our present state of knowledge, and ignorance, of the answers to them. We will limit ourselves to the statement of facts, without any indication of proof. Thus the reader will have to consult the references to find out how geometric topology has contributed to our knowledge in this area. But we hope this overview can supply a framework for a more detailed investigation of this important and, as we shall see, very active branch of fixed point theory.
Słowa kluczowe
Rocznik
Tom
49
Numer
1
Strony
19-27
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A.
Bibliografia
  • [1] D. Anosov, The Nielsen number of maps of nilmanifolds, Russian Math. Surveys 40 (1985), 149-150.
  • [2] M. Bestvina and M. Handel, Train tracks for surface homeomorphisms, Topology 34 (1995), 109-140.
  • [3] R. Brown, The Lefschetz Fixed Point Theorem, Scott-Foresman, 1971.
  • [4] R. Brown, Wecken properties for manifolds, in: Proceedings of the Conference on Nielsen Theory and Dynamical Systems, Contemp. Math. 152, 1993, 9-21.
  • [5] R. Brown and B. Sanderson, Fixed points of boundary-preserving maps of surfaces, Pacific J. Math. 158 (1993), 243-264.
  • [6] O. Davey, E. Hart and K. Trapp, Computation of Nielsen numbers for maps of closed surfaces, Trans. Amer. Math. Soc. (to appear).
  • [7] D. Dimovski, One-parameter fixed point indices, Pacific J. Math. 164 (1994), 263-297.
  • [8] D. Dimovski and R. Geoghegan, One-parameter fixed point theory, Forum Math. 2 (1990), 125-154.
  • [9] E. Fadell and S. Husseini, The Nielsen number on surfaces, in: Proceedings of the Special Session on Fixed Point Theory, Contemp. Math. 21, 1983, 59-98.
  • [10] R. Geoghegan and A. Nicas, Parametrized Lefschetz-Nielsen fixed point theory and Hochschild homology traces, Amer. J. Math. 116 (1994), 397-446.
  • [11] J. Harrison and J. Stasheff, Families of H-spaces, Quart. J. Math. 22 (1971), 347-351.
  • [12] B. Jiang, Estimation of the Nielsen numbers, Chinese Math. 5 (1964), 330-339.
  • [13] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, 1983.
  • [14] B. Jiang, Fixed points and braids, II, Math. Ann. 272 (1985), 249-256.
  • [15] B. Jiang, Commutativity and Wecken properties for fixed points of surfaces and 3-manifolds, Topology Appl. 53 (1993), 221-228.
  • [16] B. Jiang and J. Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993), 67-89.
  • [17] M. Kelly, Minimizing the number of fixed points for self-maps of compact surfaces, Pacific J. Math. 126 (1987), 81-123.
  • [18] M. Kelly, Minimizing the cardinality of the fixed point set for selfmaps of surfaces with boundary, Mich. Math. J. 39 (1992), 201-217.
  • [19] M. Kelly, The relative Nielsen number and boundary-preserving surface maps, Pacific J. Math. 161 (1993), 139-153.
  • [20] M. Kelly, The Nielsen number as an isotopy invariant, Topology Appl. 62 (1995), 127-143.
  • [21] M. Kelly, Nielsen numbers and homeomorphisms of geometric 3-manifolds, Topology Proc. 19 (1994), 149-160.
  • [22] M. Kelly, Computing Nielsen numbers of surface homeomorphisms, Topology 35 (1996), 13-25.
  • [23] E. Keppelmann and C. McCord, The Anosov theorem for exponential solvmanifolds, Pacific J. Math. 170 (1995), 143-159.
  • [24] T. Kiang, The Theory of Fixed Point Classes, Springer, 1989.
  • [25] C. McCord, Computing Nielsen numbers, in: Proceedings of the Conference on Nielsen Theory and Dynamical Systems, Contemp. Math. 152, 1993, 249-267.
  • [26] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927), 189-358.
  • [27] J. Nolan, Fixed points of boundary-preserving maps of punctured discs, Topology Appl. (to appear).
  • [28] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473.
  • [29] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.
  • [30] J. Wagner, Classes of Wecken maps of surfaces with boundary, Topology Appl. (to appear).
  • [31] J. Wagner, An algorithm for calculating the Nielsen number on surfaces with boundary, preprint.
  • [32] F. Wecken, Fixpunktklassen, III, Math. Ann. 118 (1942), 544-577.
  • [33] P. Wong, Equivariant Nielsen numbers, Pacific J. Math. 159 (1993), 153-175.
  • [34] P. Wong, Fixed point theory for homogeneous spaces, Amer. J. Math. 120 (1998), 23-42.
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Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv49i1p19bwm
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