Loops on surfaces, Feynman diagrams, and trees
High Energy Physics - Theory
2009-11-10 v6 Geometric Topology
Quantum Algebra
Abstract
We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative) Hopf algebra of pointed loops on a surface. In the last version I added sections on Wilson loops and knot diagrams.
Cite
@article{arxiv.hep-th/0403266,
title = {Loops on surfaces, Feynman diagrams, and trees},
author = {Vladimir Turaev},
journal= {arXiv preprint arXiv:hep-th/0403266},
year = {2009}
}
Comments
13 pages, no figures. Added sections on Hopf algebras, Wilson loops on surfaces and knot diagrams