Skip to main content
SpringerLink
Log in

On Lefschetz periodic point free self-maps

  • Published:
Journal of Fixed Point Theory and Applications Aims and scope Submit manuscript

Abstract

We study the periodic point free maps and Lefschetz periodic point free maps on connected retract of a finite simplicial complex using the Lefschetz numbers. We put special emphasis in the self-maps on the product of spheres and of the wedge sums of spheres.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alsedà, Ll, Baldwin, S., Llibre, J., Swanson, R., Szlenk, W.: Torus maps and Nielsen numbers. Contemp. Math. 152, 1–7 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brooks, R.B., Brown, R.F., Pak, J., Taylor, D.: Nielsen numbers of maps of tori. Proc. Am. Math. Soc. 52, 398–400 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brown, R.F.: The Lefschetz fixed point theorem. Scott, Foresman and Company, Glenview, IL (1971)

  4. Franks, J.: Homology and dynamical systems, CBSM Regional Conf. Ser. in Math., vol. 49. Am. Math. Soc., Providence, R.I. (1982)

  5. Graff, G., Kaczkowska, A., Nowak-Przygodzki, P., Signerska, J.: Lefschetz periodic point free self-maps of compact manifolds, Topol. Appl. 159, 2728–2735 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Guirao, J.L.G., Llibre, J.: On the Lefschetz periodic point free continuous self-maps on connected compact manifolds. Topol. Appl. 158, 2165–2169 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hatcher, A.: Algebraic topology. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  8. Jiang, B., Llibre, J.: Minimal sets of periods for torus maps. Discret. Contin. Dyn. Syst. 4, 301–320 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jezierski, J.: A sufficient condition for the realizability of the least number of periodic points of a smooth map. J. Fixed Point Theory Appl. 18, 609–626 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jezierski, J., Marzantowicz, W.: Homotopy Methods in Topological Fixed and Periodic Points Theory. Springer, Berlin (2006)

    MATH  Google Scholar 

  11. Lefschetz, S.: Intersections and transformations of complexes and manifolds. Trans. Am. Math. Soc. 28, 1–49 (1926)

    Article  MathSciNet  MATH  Google Scholar 

  12. Llibre, J.: Periodic point free continuous self-maps on graphs and surfaces. Topol. Appl. 159, 2228–2231 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Llibre, J., Sirvent, V.F.: Partially periodic point free self-maps on surfaces, graphs, wedge sums and product of spheres. J. Differ. Equ. Appl. 19, 1654–1662 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Vick, JW: Homology Theory. An Introduction To Algebraic Topology. Springer, Academic, New York, (1994)

Download references

Acknowledgements

The first author is partially supported by a FEDER-MINECO Grant MTM2016-77278-P, a MINECO Grant MTM2013-40998-P, and an AGAUR Grant number 2014SGR-568.

Author information

Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalunya, Spain

    Jaume Llibre

  2. Departamento de Matemáticas, Universidad Simón Bolívar, Apartado, 89000, Caracas 1086-A, Venezuela

    Víctor F. Sirvent

Authors
  1. Jaume Llibre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Víctor F. Sirvent
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Víctor F. Sirvent.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Llibre, J., Sirvent, V.F. On Lefschetz periodic point free self-maps. J. Fixed Point Theory Appl. 20, 38 (2018). https://doi.org/10.1007/s11784-018-0498-5

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s11784-018-0498-5

Keywords

Mathematics Subject Classification

Search

Navigation