#### Volume 6, issue 2 (2006)

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Labeled binary planar trees and quasi-Lie algebras

### Jerome Levine

Algebraic & Geometric Topology 6 (2006) 935–948
 arXiv: math.GT/0504278
##### Abstract

We study the natural map $\eta$ between a group of binary planar trees whose leaves are labeled by elements of a free abelian group $H$ and a certain group $\mathsf{D}\left(H\right)$ derived from the free Lie algebra over $H$. Both of these groups arise in several different topological contexts. $\eta$ 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.
Primary: 57N10
Secondary: 57M25