Geodesic
Formality of the complements of subspace arrangements with geometric lattices
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 235-247 
E. M. Feichtner; S. A. Yuzvinskii. Formality of the complements of subspace arrangements with geometric lattices. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 235-247. http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a12/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] E. Brieskorn, “Sur les groupes de tresses”, Séminaire Bourbaki, 1971–1972, No 401, Lecture Notes in Mathematics, 317, Springer-Verlag, 1973, 21–44 | MR

[2] C. De Concini, C. Procesi, “Wonderful models of subspace arrangements”, Selecta Math., 1 (1995), 459–494 | DOI | MR | Zbl

[3] J. Folkman, “The homology groups of a lattice”, J. Math. and Mech., 15 (1966), 631–636 | MR | Zbl

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

[5] J. Morgan, “The algebraic topology of smooth algebraic varieties”, Publ. Math. IHES, 48 (1978), 137–204 | MR | Zbl

[6] S. Papadima, A. Suciu, “Homotopy Lie algebras, lower central series and the Koszul property”, Geometry and Topology, 8 (2004), 1079–1125 | DOI | MR | Zbl

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

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

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

[10] S. Yuzvinsky, “Small rational model of subspace complement”, Trans. Amer. Math. Soc., 354:5 (2002), 1921–1945 | DOI | MR | Zbl