On the group-like behaviour of the Le-Murakami-Ohtsuki invariant

Abstract

We study the effect of Feynman integration and diagrammatic differential operators on the structure of group-like elements in the algebra generated by coloured vertex-oriented uni-trivalent graphs. We provide applications of our results to the study of the LMO invariant, a quantum invariant of manifolds. We also indicate further situations in which our results apply and may prove useful. The enumerative approach that we adopt has a clarity that has enabled us to perceive a number of generalizations.

Typos and minor mistakes corrected

References in corpus (2)

• Two applications of elementary knot theory to Lie algebras and Vassiliev invariants
• The Aarhus integral and the mu-invariants

Cited by in corpus (3)

• A functorial LMO invariant for Lagrangian cobordisms
• Enumeration of Graded (3+1)-Avoiding Posets
• Splitting formulas for the rational lift of the Kontsevich integral