Labeled binary planar trees and quasi-Lie algebras

Levine, Jerome

doi:10.2140/agt.2006.6.935

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Labeled binary planar trees and quasi-Lie algebras

Jerome Levine

Algebraic & Geometric Topology 6 (2006) 935–948

DOI: 10.2140/agt.2006.6.935

arXiv: math.GT/0504278

Abstract

We study the natural map $η$ between a group of binary planar trees whose leaves are labeled by elements of a free abelian group $H$ and a certain group $D (H)$ derived from the free Lie algebra over $H$ . Both of these groups arise in several different topological contexts. $η$ is known to be an isomorphism over $ℚ$ , but not over $ℤ$ . We determine its cokernel and attack the conjecture that it is injective.

This paper, Jerome Levine's fourth contribution to Algebraic and Geometric Topology, is published posthumously, following the author's untimely death in April 2006. The editors are very grateful to Kent Orr for preparing and proofreading the final version.

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

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Publication

Received: 23 December 2005

Accepted: 2 May 2006

Published: 9 August 2006

Authors

Jerome Levine
Department of Mathematics Brandeis University Waltham MA 02454-9110 USA
http://php.indiana.edu/~korr/

Volume 6, issue 2 (2006)