Algebraic & Geometric Topology

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

Gery Debongnie

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A subspace arrangement in l is a finite set A of subspaces of l. The complement space M(A) is lxAx. If M(A) is elliptic, then the homotopy Lie algebra π(ΩM(A)) 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)) where L(u,v) denotes a free Lie algebra on two generators.

Article information

Algebr. Geom. Topol., Volume 7, Number 4 (2007), 2007-2020.

Received: 10 May 2007
Revised: 9 October 2007
Accepted: 25 October 2007
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 55P62: Rational homotopy theory

homotopy Lie algebra Subspace arrangements


Debongnie, Gery. The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices. Algebr. Geom. Topol. 7 (2007), no. 4, 2007--2020. doi:10.2140/agt.2007.7.2007.

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