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On the difference between real and complex arrangements

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References

  1. [A] Arnol'd, V.I.: The cohomology ring of the colored braid group. Math. Notes5, 138–140 (1969)

    MATH  Google Scholar 

  2. [Ar] Artin, E.: Theorie der Zöpfe. Abh. Math. Semin. Univ. Hamb.4, 47–72 (1926)

    Google Scholar 

  3. [Bi] Birman, J.S.: Recent developments in braid and link theory. Math. Intell.13, 52–60 (1991)

    MATH  MathSciNet  Article  Google Scholar 

  4. [B-Z] Björner, A., Ziegler, G.M.: Combinatorial stratification of complex arrangements. J. Am. Math. Soc.5, 105–149 (1992)

    MATH  Article  Google Scholar 

  5. [Br] Brieskorn, E.: Sur le groupe de tresses (d'après V.I. Arnol'd). In: Séminaire Bourbaki 24e année 1971/72. (Lect. Notes Math., vol. 317, pp. 21–44), Berlin, Heidelberg, New York: Springer 1973

    Chapter  Google Scholar 

  6. [F1] Falk, M.J.: On the algebra associated with a geometric lattice. Adv. Math.80, 152–163 (1990)

    MATH  Article  MathSciNet  Google Scholar 

  7. [F2] Falk, M.J.: The minimal model of the complement of an arrangement of hyperplanes. Trans. Am. Math. Soc.309, 543–556 (1988)

    MATH  Article  MathSciNet  Google Scholar 

  8. [Go-MP] Goresky, M., MacPherson, R.D.: Stratified Morse Theory. (Ergeb. Math. Grenzgeb., 3. Folge, Bd. 14) Berlin, Heidelberg, New York: Springer 1988

    MATH  Google Scholar 

  9. [Gr-M] Griffiths, P.A., Morgan, J.W., Rational Homotopy Theory and Differential Forms. (Prog. Math., vol. 16) Boston, Birkhäuser 1981

    MATH  Google Scholar 

  10. [J-O-S] Jewell, K., Orlik, P., Shapiro, B.Z.: On the cohomology of complements to arrangements of affine subspaces. (Preprint 1991)

  11. [M] Mazurovskii, V.F.: Kauffmann polynomials of non-singular configurations of projective lines. Russ. Math. Surv.44, 212–213 (1989)

    Article  MathSciNet  Google Scholar 

  12. [O] Orlik, P., Introduction to Arrangements. (CBMS Reg. Conf. Ser. Math., vol. 72) Providence, RI: Am. Math. Soc. 1989

    Google Scholar 

  13. [O-S] Orlik, P., Solomon, L., Combinatorics and topology of complements of hyperplanes. Invent. Math.56, 167–189 (1980)

    MATH  Article  MathSciNet  Google Scholar 

  14. [R] Rolfsen, D., Knots and Links. (Math. Lect. Notes Ser., vol. 7) Berkeley, CA: Publish or Perish 1976

    MATH  Google Scholar 

  15. [Va] Vassiliev, V.A.: Complements to discriminants of smooth mappings. Conference notes. Trieste: International Centre for Theoretical Physics 1991

    Google Scholar 

  16. [Vi] Viro, O.Ya.: Topological problems concerning lines and points of three-dimensional space. Sov. Math., Dokl.32, 528–531 (1985)

    MATH  Google Scholar 

  17. [Vi-D] Viro, O.Ya., Drobotukhina, Yu.V.: Configurations of skew lines. Leningr. Math. J.1, 1027–1050 (1990)

    MATH  MathSciNet  Google Scholar 

  18. [Z] Ziegler, G.M.: Combinatorial Models for Subspace Arrangements. Habilitationsschrift, TU Berlin (April 1992)

  19. [Z-Ž] Ziegler, G.M., Živaljević, R.T.: Homotopy types of arrangements via diagrams of spaces. Report No. 10 (1991/92), Djursholm: Institut Mittag-Leffler 1991, Math. Ann. (to appear)

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Ziegler, G.M. On the difference between real and complex arrangements. Math Z 212, 1–11 (1993). https://doi.org/10.1007/BF02571638

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Keywords

  • Fundamental Group
  • Homotopy Type
  • Intersection Lattice
  • Cohomology Algebra
  • Complex Arrangement