6 problems

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 $\Sigma$ be a closed, orientable $3$-manifold. Write $\lambda_{\operatorname{PSL}_2(\mathbb C)}(\Sigma)$ and $\lambda_{\operatorname{SL}_2(\mathbb C)}(\Sigma)$ for the respecti…

Finite-type conjecture for $\tau$. The invariant $\tau$ is a finite type invariant.

Let $T$ be a knot, let $X(T,1/K)$ denote the corresponding $1/K$ Dehn surgery, and let $\Lambda_{SU(3)}(X(T,1/K))$ be its SU(3)-knot invariant. Write $\Delta_T$ for the normalized…

Let $\operatorname{SU}(n)$ Casson invariants be the gauge-theoretic invariants associated with $\operatorname{SU}(n)$ representations, and let the generalized SeibergWitten equatio…

Sign conjecture. For every $f\in R^{\rm zd}(\Sigma(m,p,q))$, the quantity $\varepsilon_f$ is negative. Consequently,