Advertisement

Journal of Mathematical Sciences

, Volume 91, Issue 6, pp 3532–3541 | Cite as

Projective graph theory and configurations of lines

  • S. I. Khashin
Article

Abstract

The spaces of disjoint configurations of k-dimensional subspaces in ℝP 2k+1 (for example, lines in ℝP 3) are studied. These spaces are modeled by various simplicial schemes, and the homology groups of the latter are computed in certain cases. We use the fact that every configuration can be assigned a so-called projective graph, which is a class of graphs with respect to a certain equivalence relation. Bibliography: 5 titles.

Keywords

Chain Complex Geometric Realization Isotopy Class Projective Graph Matrix Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Ya. Viro, “Topological problems concerning lines and points of three-dimensional space,”Dokl. Akad. Nauk SSSR,284, 1049–1052 (1985).MATHMathSciNetGoogle Scholar
  2. 2.
    V. F. Mazurovskii, “Nonsingular configurations ofk-dimensional subspaces of the (2k+1)-dimensional real projective space,”Vestn. Leningrad Gos. Univ., Ser. 1, No. 3, 21–26 (1990).MATHMathSciNetGoogle Scholar
  3. 3.
    S. I. Khashin and V. F. Mazurovskii, “Stable equivalence of real projective configurations,”Adv. Sov. Math. to appear.Google Scholar
  4. 4.
    G. D. James,The Representation Theory of Symmetric Groups, Springer-Verlag, Berlin (1978).Google Scholar
  5. 5.
    H. Crapo and R. Penne, “Chirality and the isotopy classification of the skew lines in projective 3-space,”Adv. Math.,103, 1–106.Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. I. Khashin

There are no affiliations available

Personalised recommendations