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Higher homotopy groups of complements of complex hyperplane

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S. Papadima, A.I. Suciu

Editorial: Advances in Mathematics, 165 (1), p.71-100, 2002.


We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range, and we give an explicit Z pi_1-module presentation of pi_p, the first non-vanishing higher homotopy group. We also give a combinatorial formula for the pi_1-coinvariants of pi_p.

For affine line arrangements whose cones are hypersolvable, we provide a minimal resolution of pi_2, and study some of the properties of this module. For graphic arrangements associated to graphs with no 3-cycles, we obtain information on pi_2, directly from the graph. The pi_1-coinvariants of pi_2 may distinguish the homotopy 2-types of arrangement complements with the same pi_1, and the same Betti numbers in low degrees.

Cuvinte cheie: hypersolvable arrangement, higher homotopy groups, minimal cell decomposition