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2004 Homotopy Lie algebras, lower central series and the Koszul property
Ştefan Papadima, Alexander I Suciu
Geom. Topol. 8(3): 1079-1125 (2004). DOI: 10.2140/gt.2004.8.1079


Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X. Assume H(X,) is a Koszul algebra. Then, the homotopy Lie algebra π(ΩY) equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equality is actually equivalent to the Koszulness of H(X,). If X is formal (and only then), the equality lifts to a filtered isomorphism between the Malcev completion of π1(X) and the completion of [ΩS2k+1,ΩY]. Among spaces that admit naturally defined homological rescalings are complements of complex hyperplane arrangements, and complements of classical links. The Rescaling Formula holds for supersolvable arrangements, as well as for links with connected linking graph.


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Ştefan Papadima. Alexander I Suciu. "Homotopy Lie algebras, lower central series and the Koszul property." Geom. Topol. 8 (3) 1079 - 1125, 2004.


Received: 3 March 2004; Accepted: 17 July 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1127.55004
MathSciNet: MR2087079
Digital Object Identifier: 10.2140/gt.2004.8.1079

Primary: 16S37, 20F14, 55Q15
Secondary: 20F40, 52C35, 55P62, 57M25, 57Q45

Rights: Copyright © 2004 Mathematical Sciences Publishers


Vol.8 • No. 3 • 2004
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