4 problems

Let $K$ be a knot in an integral homology $3$-sphere $M$, and let $Q_n(M,K)$ denote the $n$-loop part of the logarithm of the LMO invariant, for $n\geq 1$. Rozansky's rationality c…

Let $M$ be a 3-manifold, let $Z_n^{LMO}(M)$ denote the degree-$n$ part of the LMO invariant, and let $X$ be a hyper-Kähler manifold of dimension $4n$. Write $W_X^{RW}$ for the Roza…

Let $\LCob_q$ be the category of Lagrangian cobordisms and let $\tsA$ be the corresponding target category of Jacobi-diagram-valued objects. The LMO functor is … Its construction u…

Let $M$ be a rational homology 3-sphere, let ${\frak g}$ be a simple Lie algebra, let $\tau^{\frak g}(M)$ denote its perturbative ${\frak g}$ invariant, and let…