Skip to main content
SpringerLink
Log in

A Primer of Nielsen Fixed Point Theory

  • Chapter
Handbook of Topological Fixed Point Theory

Partially supported by a MOSTC and a MOEC grants.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. S. Alexandroff and H. Hopf, Topologie, Springer-Verlag, Berlin, 1935. (German)

    Google Scholar 

  2. J. S. Birman, Braids, links, and mapping class groups, Princeton University Press, Princeton, N.J., 1974.

    Google Scholar 

  3. L. E. J. Brouwer, Über die Minimalzahl der Fixpunkte bei den Klassen von eindeutigen stetigen Transformationen der Ringflächen, Math. Ann. 82 (1921), 94–96. (German)

    Article  Google Scholar 

  4. R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.-London, 1971.

    MATH  Google Scholar 

  5. _____, Fixed point theory, History of Topology (I. M. James, ed.), North-Holland, Amsterdam, 1999, pp. 271–299.

    Google Scholar 

  6. A. Dold, Lectures on Algebraic Topology, Springer-Verlag, New York, 1972; second ed., 1980.

    MATH  Google Scholar 

  7. E. Fadell, Nielsen numbers as a homotopy type invariant, Pacific J. Math. 63 (1976), 381–388.

    MATH  MathSciNet  Google Scholar 

  8. E. Fadell and S. Husseini, Fixed point theory for non-simply-connected manifolds, Topology 20 (1981), 53–92.

    Article  MathSciNet  MATH  Google Scholar 

  9. _____, The Nielsen number on surfaces, Topological Methods in Nonlinear Functional Analysis (Toronto, Ont., 1982), Contemp. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1983, pp. 59–98.

    Google Scholar 

  10. S. Husseini, Generalized Lefschetz numbers, Trans. Amer. Math. Soc. 272 (1982), 247–274.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. Jaco, Lectures on three-manifold topology, CBMS Regional Conf. Ser. in Math. 43 (1980), Amer. Math. Soc., Providence, R.I..

    Google Scholar 

  12. B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980), 749–763.

    MATH  MathSciNet  Google Scholar 

  13. _____, Fixed points of surface homeomorphisms, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 176–178.

    MATH  MathSciNet  Google Scholar 

  14. _____, Fixed point classes from a differential viewpoint, Fixed Point Theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, Berlin, 1981, pp. 163–170.

    Google Scholar 

  15. _____, Lectures on Nielsen fixed point theory, Contemp. Math. 14 (1983), Amer. Math. Soc.

    Google Scholar 

  16. _____, Fixed points and braids, Invent. Math. 75 (1984), 69–74.

    Article  MATH  MathSciNet  Google Scholar 

  17. _____, Fixed points and braids II, Math. Ann. 272 (1985), 249–256.

    Article  MATH  MathSciNet  Google Scholar 

  18. _____, A characterization of fixed point classes, Fixed Point Theory and its Applications, Contemp. Math. (Berkeley, CA, 1986), vol. 72, Amer. Math. Soc., Providence, RI, 1988, pp. 157–160.

    Google Scholar 

  19. _____, Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996), 151–185.

    MATH  MathSciNet  Google Scholar 

  20. B. Jiang and J. Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993), 67–89.

    MathSciNet  MATH  Google Scholar 

  21. B. Jiang, Sh. Wang and Y.-Q. Wu, Homeomorphisms of 3-manifolds and the realization of Nielsen number, Comm. Anal. Geom. 9 (2001), 825–877.

    MathSciNet  MATH  Google Scholar 

  22. M. R. Kelly, The Nielsen number as an isotopy invariant, Topology Appl. 62 (1995), 127–143.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. A. Kervaire, Geometric and algebraic intersection numbers, Comment. Math. Helv. 39 (1965), 271–280.

    MATH  MathSciNet  Google Scholar 

  24. T.-h. Kiang, The Theory of Fixed Point Classes, Springer—Verlag, Berlin, 1989.

    MATH  Google Scholar 

  25. T.-h. Kiang and B. Jiang, The Nielsen numbers of self-mappings of the same homotopy type, Sci. Sinica 12 (1963), 1071–1072.

    MathSciNet  MATH  Google Scholar 

  26. W. S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace & World, Inc., New York, 1967.

    MATH  Google Scholar 

  27. J. Nielsen, Über die Minimalzahl der Fixpunkte bei den Abbildungstypen der Ringflächen, Math. Ann. 82 (1921), 83–93. (German)

    Article  Google Scholar 

  28. _____, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, I, Acta Math. 50 (1927), 189–358 (German); English transl. V. L. Hansen (ed.), Investigations in the topology of closed orientable surfaces, I, Jakob Nielsen: Collected Mathematical Papers, vol. 1, Birkhäuser, Boston, 1986, pp. 223–341.

    Article  MATH  MathSciNet  Google Scholar 

  29. K. Reidemeister,Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), 586–593. (German)

    Google Scholar 

  30. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401–487.

    MATH  MathSciNet  Google Scholar 

  31. H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459–473.

    MATH  MathSciNet  Google Scholar 

  32. G. Shi, Least number of fixed points of the identity class, Acta Math. Sinica 18 (1975), 192–202 (Chinese); an English exposition can be found in Chapter 4 of [Ki]

    MATH  Google Scholar 

  33. W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), 417–431.

    Article  MATH  MathSciNet  Google Scholar 

  34. F. Wecken, Fixpunktklassen, I, Math. Ann. 117 (1941), 659–671. (German)

    Article  MATH  MathSciNet  Google Scholar 

  35. _____, Fixpunktklassen, II, Homotopieinvarianten der Fixpunkttheorie, Math. Ann. 118 (1941), 216–234. (German)

    Article  MATH  MathSciNet  Google Scholar 

  36. _____, Fixpunktklassen, III, Mindestzahlen von Fixpunkten, Math. Ann. 118 (1942), 544–577. (German)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Boju Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Los Angeles, USA

    R. F. Brown

  2. Department of Applied Mathematics ‘G. Sansone', Florence, Italy

    M. Furi

  3. Juliusz Schauder Center of the Nicolaus Copernicus University, Poland

    L. Górniewicz

  4. Department of Mathematics, Peking University, Beijing, China

    B. Jiang

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer

About this chapter

Cite this chapter

Jiang, B. (2005). A Primer of Nielsen Fixed Point Theory. In: Brown, R.F., Furi, M., Górniewicz, L., Jiang, B. (eds) Handbook of Topological Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3222-6_16

Download citation

Publish with us

Policies and ethics

Search

Navigation