The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices

Debongnie, Gery
(2007) Algebraic And Geometric Topology — Vol. 7, p. 2007-2020 (2007)

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  • Debongnie, GeryUCLouvain
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Abstract
A subspace arrangement in C-l is a finite set A of subspaces of C-l. The complement space M(A) is C-l U-x is an element of AX. If M(A) is elliptic, then the homotopy Lie algebra pi(star)(Omega M(A))circle times 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) -> pi(Omega M(A)) circle times Q where L(u, v) denotes a free Lie algebra on two generators.
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Debongnie, G. (2007). The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices. Algebraic And Geometric Topology, 7, 2007-2020. https://doi.org/10.2140/agt.2007.7.2007 (Original work published 2007)