%0 Journal Article %T Homotopy Lie algebra of the complements of subspace arrangements with geometric lattices %A G. Debongnie %J Mathematics %D 2007 %I arXiv %X Let A be a geometric arrangement such that codim(x) > 1 for every x in A. We prove that, if the complement space M(A) is rationally hyperbolic, then there exists an injective from a free Lie algebra L(u,v) to the homotopy Lie algebra of M(A). %U http://arxiv.org/abs/0705.1451v1