The degree 2 part of the LMO invariant of cyclic branched covers of knots obtained by plumbing the doubles of two knots

Abstract

The LMO invariant is a universal quantum invariant of 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.