Paper published by Geometry and Topology

From: Geometry and Topology Journal (gt_at_maths.warwick.ac.uk)
Date: 08/22/04 

Date: 22 Aug 2004 08:45:00 -0400

The following paper has been published:

Geometry and Topology, Volume 8 (2004) Paper no. 30, pages 1079--1125

URL:
http://www.maths.warwick.ac.uk/gt/GTVol8/paper30.abs.html

Title:
Homotopy Lie algebras, lower central series and the Koszul property

Author(s):
Stefan Papadima, Alexander I Suciu

Abstract:

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,Q) is a
Koszul algebra. Then, the homotopy Lie algebra pi_*(Omega Y) tensor Q
equals, up to k-rescaling, the graded rational Lie algebra associated
to the lower central series of pi_1(X). If Y is a formal space, this
equality is actually equivalent to the Koszulness of H^*(X,Q). If X is
formal (and only then), the equality lifts to a filtered isomorphism
between the Malcev completion of pi_1(X) and the completion of [Omega
S^{2k+1} ,Omega Y]. 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.

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

Keywords:
Homotopy groups, Whitehead product, rescaling, Koszul algebra, lower
central series, Quillen functors, Milnor--Moore group, Malcev
completion, formal, coformal, subspace arrangement, spherical link

Received: 3 March 2004
Accepted: 17 July 2004
Published: 22 August 2004

Proposed: Haynes Miller
Seconded: Thomas Goodwillie, Steven Ferry

Author(s) address(es):
Institute of Mathematics of the Romanian Academy
PO Box 1-764, RO-014700 Bucharest, Romania
and
Department of Mathematics, Northeastern University
Boston, MA 02115, USA

Email: stefan.papadima@imar.ro, a.suciu@neu.edu