Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 4 (2007), 2007-2020.
The homotopy Lie algebra of the complements of subspace arrangements with geometric lattices
A subspace arrangement in is a finite set of subspaces of . The complement space is . If is elliptic, then the homotopy Lie algebra is finitely generated. In this paper, we prove that if is a geometric arrangement such that is a hyperbolic 1–connected space, then there exists an injective map where denotes a free Lie algebra on two generators.
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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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P62: Rational homotopy theory
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. https://projecteuclid.org/euclid.agt/1513796781