We study the natural map between a group of binary planar trees whose leaves are labeled by elements of a free abelian group and a certain group derived from the free Lie algebra over . Both of these groups arise in several different topological contexts. is known to be an isomorphism over , but not over . We determine its cokernel and attack the conjecture that it is injective.
"Labeled binary planar trees and quasi-Lie algebras." Algebr. Geom. Topol. 6 (2) 935 - 948, 2006. https://doi.org/10.2140/agt.2006.6.935