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Formality of the complements of subspace arrangements with geometric lattices

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Abstract

We show that for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal as a differential graded algebra. Bibliography: 10 titles.

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References

  1. E. Brieskorn, “Sur les groupes de tresses,” Séminaire Bourbaki, 1971/1972, Exp. No. 401; Lect. Notes Math., 317, 21–44 (1973).

  2. C. De Concini and C. Procesi, “Wonderful models of subspace arrangements,” Selecta Math., 1, 459–494 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Folkman, “The homology groups of a lattice,” J. Math. Mech., 15, 631–636 (1966).

    MATH  MathSciNet  Google Scholar 

  4. M. Goresky and R. MacPherson, Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 14, Springer-Verlag, Berlin (1988).

    MATH  Google Scholar 

  5. J. Morgan, “The algebraic topology of smooth algebraic varieties,” Inst. Hautes Études Sci., Publ. Math., 48, 137–204 (1978).

    MATH  Google Scholar 

  6. S. Papadima and A. Suciu, “Homotopy Lie algebras, lower central series and the Koszul property,” Geom. Topol., 8, 1079–1125 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Yuzvinsky, “Rational model of subspace complement on atomic complex,” Publ. Inst. Math. (Beograd) (N.S.), 66(80), 157–164 (1999).

    MathSciNet  Google Scholar 

  8. S. Yuzvinsky, “Taylor and minimal resolutions of homogenous polynomial ideals,” Math. Res. Lett., 6, 779–793 (1999).

    MATH  MathSciNet  Google Scholar 

  9. S. Yuzvinsky, “Orlik-Solomon algebras in algebra and topology,” Russian Math. Surveys, 56, 293–364 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Yuzvinsky, “Small rational model of subspace complement,” Trans. Amer. Math. Soc., 354, No. 5, 1921–1945 (2002).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, ETH Zurich, Switzerland

    E. M. Feichtner

  2. Department of Mathematics, University of Oregon, USA

    S. Yuzvinsky

Authors
  1. E. M. Feichtner
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  2. S. Yuzvinsky
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 235–247.

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Feichtner, E.M., Yuzvinsky, S. Formality of the complements of subspace arrangements with geometric lattices. J Math Sci 140, 472–479 (2007). https://doi.org/10.1007/s10958-007-0454-1

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  • DOI: https://doi.org/10.1007/s10958-007-0454-1

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