Pacific Journal of Mathematics

Fixed points of surface diffeomorphisms.

Jian Han Guo and Bo Ju Jiang

Article information

Source
Pacific J. Math., Volume 160, Number 1 (1993), 67-89.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102624565

Mathematical Reviews number (MathSciNet)
MR1227504

Zentralblatt MATH identifier
0829.55001

Subjects
Primary: 57N05: Topology of $E^2$ , 2-manifolds
Secondary: 57M20: Two-dimensional complexes 57R50: Diffeomorphisms

Citation

Jiang, Bo Ju; Guo, Jian Han. Fixed points of surface diffeomorphisms. Pacific J. Math. 160 (1993), no. 1, 67--89. https://projecteuclid.org/euclid.pjm/1102624565


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References

  • [B] L. Bers, An extremal problem for quasiconformal mapping and a theorem by Thurston, Acta Math., 141 (1978), 73-98.
  • [BK] J. S. Birman and M. Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces,Adv. in Math., 46 (1982), 217-220.
  • [Br] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott-Foresman, Chicago, 1971.
  • [E] D. B. A. Epstein, Curveson 2-manifoldsand isotopies,Acta Math., 115(196?), 83-107.
  • [FLP] A. Fathi, F. Laudenbach, and V. Poenaru, Travaux de Thurston sur les sur- faces, Sminaire Orsay,Asterisque vol. 66-67, Soc. Math. France, Paris, 1979.
  • [GK] M. Gerber and A. Katok, Smooth models of Thurston's pseudo-Anosov maps, Ann. Sci. Ec. Norm. Sup., 15 (1982), 173-204.
  • [HT] M.Handel and W. P.Thurston, New proofs of some results of Nielsen, Adv. in Math., 56(1985), 173-191.
  • [I] N.V. Ivanov, Nielsen numbers of self-maps of surfaces, Studies in Topology IV, Zap. Nauchn.Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), vol.122, Nauka, Leningrad, 1982, pp. 56-65, 163-164 (Russian); English transl., J. Sov. Math., 26 (1984), 1636-1641.
  • [Jl] B.Jiang, Fixed point classesfrom a differential viewpoint, Fixed Point Theory (E. Fadell, G.Fournier, eds.), Lecture Notes in Math., vol. 886, Springer- Verlag, Berlin, Heidelberg, New York, 1981, pp. 163-170.
  • [J2] B.Jiang, Fixed points of surface homeomorphisms, Bull. Amer. Math. Soc, 5 (1981), 176-178.
  • [J3] B.Jiang,Lectures onNielsen Fixed Point Theory, Contemp.Math.,vol. 14, Amer. Math. Soc, Providence, RI, 1983.
  • [J4] B.Jiang, Fixed points andbraids, Invent. Math., 75 (1984), 69-74; II, Math. Ann., 272(1985), 249-256.
  • [K] T.-H. Kiang, The Theory ofFixed Point Classes, Science Press, Beijing,1979, 1986 (Chinese); English edition, 1989, Springer-Verlag, Berlin, Heidelberg, New York.
  • [Nl] J.Nielsen, Uber dieMinimalzahl derFixpunkte beiden Abbildungstypen der Ringflchen, Math. Ann., 82 (1921), 83-93.
  • [N2] J.Nielsen, Untersuchungen zurTopologiedes geschlossenen zweiseitigen Flchen, I, Acta Math.,50(1927), 189-358; English transl., Investigations inthe topology of closed orientable surfaces, I,Jakob Nielsen: Collected Mathematical Papers (V.L. Hansen, ed.), vol. 1,Birkhauser, Boston, 1986, pp. 223-341.
  • [S] H. Schirmer,A relative Nielsen number, Pacific J. Math., 122 (1986), 459-473.
  • [T] W.P. Thurston, Onthe geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc, 19 (1988), 417-431.
  • [W] F.Wecken, Fixpunktklassen, I,Math. Ann., 117(1941), 659-671; II,Math. Ann., 118(1942), 216-234; III,Math. Ann., 118(1942), 544-577.
  • [Wu] Y.-Q. Wu, Canonical reducing curves of surface homeomorphisms, Acta Math. Sinica, New Series, 3 (1987), 305-313.
  • [Z] X.-Z. Zhao,A relative Nielsen number for thecomplement, Topological Fixed Point Theory and Applications (B. Jiang, ed.), Lecture Notes in Math., vol. 1411, Springer-Verlag, Berlin, Heidelberg, New York, 1989, pp. 189-199.