Skip to main content
Log in

Winding numbers on surfaces. II

Applications

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Birman, Joan: Automorphisms of the fundamental group of a closed, orientable 2-manifold. Proc. Amer. Math. Soc.21, 351–354 (1969).

    Google Scholar 

  2. Birman, J., Hilden, M.: Mapping class groups of closed surfaces as covering spaces. Annals of Math. Studies66, Princeton 1971.

  3. CĂlugĂreanu, G.: Sur les courbes fermées simples tracées sur une surface fermée orientable. Mathematika (Cluj)8(31, 29–38 (1966).

    Google Scholar 

  4. Chillingworth, D. R. J.: Thesis, University of Cambridge 1968.

  5. Chillingworth, D. R. J.: A finite set of generators for the homeotopy group of a non-orientable surface. Proc. Cambridge Philos. Soc.65, 409–430 (1969).

    Google Scholar 

  6. Chillingworth, D. R. J.: Simple closed curves on surfaces. Bull. London Math. Soc.1, 310–314 (1969).

    Google Scholar 

  7. Chillingworth, D. R. J.: Winding numbers on surfaces, I. Math. Ann.196, 218–249 (1972).

    Google Scholar 

  8. Dehn, M.: Transformation der Kurven auf zweiseitigen Flächen. Math. Ann.72, 413–421 (1912).

    Google Scholar 

  9. Dehn, M.: Die Gruppen der Abbildungsklassen. Acta Math.69, 135–206 (1936).

    Google Scholar 

  10. Epstein, D. B. A.: Curves on 2-manifolds and isotopies. Acta Math.115, 83–107 (1966).

    Google Scholar 

  11. Lickorish, W. B. R.: A representation of orientable combinational 3-manifolds. Ann. Math.76, 531–540 (1962).

    Google Scholar 

  12. Lickorish, W. B. R.: Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc.59, 307–317 (1963).

    Google Scholar 

  13. Lickorish, W. B. R.: A finite set of generators for the homeotopy group of a 2-manifold. Proc. Cambridge Philos. Soc.60, 769–778 (1964). Corrigendum, Proc. Cambridge Philos. Soc.62, 679–681 (1966).

    Google Scholar 

  14. Lickorish, W. B. R.: On the homeomorphisms of a nonorientable surface. Proc. Cambridge Philos. Soc.61, 61–64 (1965).

    Google Scholar 

  15. Reidermeister, K.: Einführung in die kombinatorische Topologie. New York: Chelsea Publishing Company 1950.

    Google Scholar 

  16. Reinhart, B. L.: The winding number on two manifolds. Ann. Inst. Fourier (Grenoble)10, 271–283 (1960).

    Google Scholar 

  17. Reinhart, B. L.: Algorithms for Jordan curves on compact surfaces. Ann. Math.75, 209–222 (1962).

    Google Scholar 

  18. Reinhart, B. L.: Further remarks on the winding number. Ann. Inst. Fourier (Grenoble)13, 155–160 (1963).

    Google Scholar 

  19. Zieschang, H.: Algorithmen für einfache Kurven auf Flächen. Math. Scand.17, 17–40 (1965).

    Google Scholar 

  20. Zieschang, H.: Über Automorphismen ebener diskontinuierlicher Gruppen. Math. Ann.166, 148–167 (1966).

    Google Scholar 

  21. Zieschang, H.: Algorithmen für einfache Kurven auf Flächen, II. Math. Scand.25, 49–58 (1969).

    Google Scholar 

  22. Zieschang, H., Vogt, E., Coldewey, H.-D.: Flächen und ebene diskontinuierliche Gruppen. Lecture Notes in Mathematics, No.122. Berlin-Heidelberg-New York: Springer 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chillingworth, D.R.J. Winding numbers on surfaces. II. Math. Ann. 199, 131–153 (1972). https://doi.org/10.1007/BF01431419

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01431419

Navigation