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

Gery Debongnie

Algebraic & Geometric Topology 7 (2007) 2007–2020
Abstract

A subspace arrangement in l is a finite set A of subspaces of l. The complement space M(A) is l xAx. 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.

Keywords
homotopy Lie algebra, Subspace arrangements
Mathematical Subject Classification 2000
Primary: 55P62
References
Publication
Received: 10 May 2007
Revised: 9 October 2007
Accepted: 25 October 2007
Published: 26 December 2007
Authors
Gery Debongnie
UCL, Departement de mathematique
Chemin du Cyclotron, 2
B-1348 Louvain-la-neuve
Belgium
http://www.math.ucl.ac.be/membres/debongnie/