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

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

2005-11-17

arxiv.org/abs/math/0511452v2

J. Knot Theory Ramifications 16 (2007) 699-718

Mathematics

Quantum Algebra

Typos and minor mistakes corrected

Scientific paper

10.1142/S0218216507005452

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.

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