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The degree 2 part of the LMO invariant of cyclic branched covers of knots obtained by plumbing the doubles of two knots
Preview AbstractThe LMO invariant is a universal quantum invariant of closed oriented 3-manifolds. In this paper, we present the degree 2 part of the LMO invariant of cyclic branched covers of knots by using the 3-loop invariant of knots, and we calculate it concretely for knots obtained by plumbing the doubles of two knots.
THE ÅRHUS INTEGRAL AND THE μ-INVARIANTS
Preview AbstractWe relate the tree part of the Århus integral to Milnor's μ-invariants of string-links in homology balls thus generalizing results of Habegger and Masbaum.
ON THE GROUP-LIKE BEHAVIOR OF THE LE–MURAKAMI–OHTSUKI INVARIANT
Preview AbstractWe study the effect of Feynman integration and diagrammatic differential operators on the structure of group-like elements in the algebra generated by colored 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.