Geodesic
Labeled binary planar trees and quasi-Lie algebras
Levine, Jerome1
1Department of Mathematics, Brandeis University, Waltham MA 02454-9110, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 935-948
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2006.6.935

Levine, Jerome  1

1 Department of Mathematics, Brandeis University, Waltham MA 02454-9110, USA 
@article{10_2140_agt_2006_6_935,
     author = {Levine, Jerome},
     title = {Labeled binary planar trees and {quasi-Lie} algebras},
     journal = {Algebraic and Geometric Topology},
     pages = {935--948},
     year = {2006},
     volume = {6},
     number = {2},
     doi = {10.2140/agt.2006.6.935},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.935/}
}
TY  - JOUR
AU  - Levine, Jerome
TI  - Labeled binary planar trees and quasi-Lie algebras
JO  - Algebraic and Geometric Topology
PY  - 2006
SP  - 935
EP  - 948
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.935/
DO  - 10.2140/agt.2006.6.935
ID  - 10_2140_agt_2006_6_935
ER  - 
%0 Journal Article
%A Levine, Jerome
%T Labeled binary planar trees and quasi-Lie algebras
%J Algebraic and Geometric Topology
%D 2006
%P 935-948
%V 6
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.935/
%R 10.2140/agt.2006.6.935
%F 10_2140_agt_2006_6_935
Levine, Jerome. Labeled binary planar trees and quasi-Lie algebras. Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 935-948. doi: 10.2140/agt.2006.6.935

[1] S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75

[2] S Garoufalidis, J Levine, Tree-level invariants of three-manifolds, from: "Proceedings of Stony Brook Conference in honor of Dennis Sullivan" (2005)

[3] N Habegger, X S Lin, On link concordance and Milnor’s μ invariants, Bull. London Math. Soc. 30 (1998) 419

[4] N Habegger, G Masbaum, The Kontsevich integral and Milnor’s invariants, Topology 39 (2000) 1253

[5] N Habegger, W Pitsch, Tree level Lie algebra structures of perturbative invariants, J. Knot Theory Ramifications 12 (2003) 333

[6] K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1

[7] M Hall Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575

[8] D Johnson, A survey of the Torelli group, from: "Low-dimensional topology (San Francisco, Calif., 1981)", Contemp. Math. 20, Amer. Math. Soc. (1983) 165

[9] M Kontsevich, Formal (non)commutative symplectic geometry, from: "The Gel’fand Mathematical Seminars, 1990–1992", Birkhäuser (1993) 173

[10] J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243

[11] J Levine, Addendum and correction to : “Homology cylinders : an enlargement of the mapping class group”, Algebr. Geom. Topol. 2 (2002) 1197

[12] W Magnus, A Karrass, D Solitar, Combinatorial group theory : Presentations of groups in terms of generators and relations, Interscience [John Wiley Sons] (1966)

[13] S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699

[14] K E Orr, Homotopy invariants of links, Invent. Math. 95 (1989) 379

[15] R Schneiderman, P Teichner, Whitney towers and the Kontsevich integral, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7 (2004) 101

Cité par Sources :