Skip to main content
SpringerLink
Log in

Classification of ordered nonsingular configurations of at most seven lines of ℝP 3 up to rigid isotopy

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

A projective m-configuration is a collection of m nonoriented pairwise disjoint lines in ℝP 3. An isotopy consisting of projective m-configurations is called a rigid isotopy. In the paper, the rigid isotopy classification of ordered projective m-configurations is obtained for m≤7. Bibliography: 11 titles.

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. O. Ya. Viro, “Topological problems concerning lines and points of three-dimensional space,”Dokl. Akad. Nauk SSSR,284, 1049–1052 (1985).

    MATH  MathSciNet  Google Scholar 

  2. V. F. Mazurovskii, “Configurations of six skew lines,”Zap. Nauchn. Semin. LOMI,167, 121–134 (1988).

    MATH  Google Scholar 

  3. V. F. Mazurovskii, “Configurations of at most 6 lines of ℝP3,”Lect. Notes Math.,1524, 354–371 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Borobia and V. F. Mazurovskii, “Nonsingular configurations of 7 lines of ℝP3,” Uppsala Univ. Preprint (1995).

  5. S. I. Khashin and V. F. Mazurovskii, “Stable equivalence of real projective configurations,”Adv. Sov. Math. to appear.

  6. R. Penne, “Lines in 3-space: isotopy, chirality and weavings,” Ph.D. Thesis, Antwerp Univ. (1992).

  7. L. H. Kauffman, “State models and the Jones polynomial,”Topology,26, 395–407 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  8. Yu. V. Drobotukhina, “An analogue of the Jones polynomial for links in ℝP 3 and a generalization of the Kauffman-Murasugi theorem,”Algebra Analiz,2, No. 3, 171–191 (1990).

    MATH  MathSciNet  Google Scholar 

  9. V. F. Mazurovskii, “Kauffman polynomials of nonsingular configurations of projective lines,”Usp. Mat. Nauk,44, No. 5, 173–174 (1989).

    MATH  MathSciNet  Google Scholar 

  10. A. Borobia and V. F. Mazurovskii, “On diagrams of configurations of 7 skew lines of ℝ3,”Adv. Sov. Math. to appear.

  11. R. Penne, “Multi-variable Burau matrices and labeled line configurations,”J. Knot Theory Ramifications,4, 235–262 (1995).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. V. F. Mazurovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. B. Pavlov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 269–285.

Translated by V. F. Mazurovskii.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mazurovskii, V.F., Pavlov, N.B. Classification of ordered nonsingular configurations of at most seven lines of ℝP 3 up to rigid isotopy. J Math Sci 91, 3508–3517 (1998). https://doi.org/10.1007/BF02434929

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02434929

Keywords

Search

Navigation