Geodesic
The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices
Debongnie, Gery1
1UCL, Departement de mathematique, Chemin du Cyclotron, 2, B-1348 Louvain-la-neuve, Belgium
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2007-2020
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A subspace arrangement in ℂl is a finite set A of subspaces of ℂl. The complement space M(A) is ℂl ∖∪x∈Ax. If M(A) is elliptic, then the homotopy Lie algebra π⋆(ΩM(A)) ⊗ ℚ is finitely generated. In this paper, we prove that if A is a geometric arrangement such that M(A) is a hyperbolic 1–connected space, then there exists an injective map L(u,v) → π⋆(ΩM(A)) ⊗ ℚ where L(u,v) denotes a free Lie algebra on two generators.

DOI : 10.2140/agt.2007.7.2007
Keywords: homotopy Lie algebra, Subspace arrangements

Debongnie, Gery  1

1 UCL, Departement de mathematique, Chemin du Cyclotron, 2, B-1348 Louvain-la-neuve, Belgium 
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Debongnie, Gery. The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2007-2020. doi: 10.2140/agt.2007.7.2007

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