3 problems

Let $K_m=T(7,17,2,10m-4)$, and let $(V,W)$ be the unique minimal genus-two Heegaard splitting of its exterior $E(K_m)=S^3-N(K_m)$. Let $(V',W')$ be the boundary stabilization of…

Let $K=T(p,q,2,r)$ be a twisted torus knot, let $E(K)=S^3-N(K)$ be its exterior, and suppose that $K$ is not $5cmu$-primitive. The unique genus-two splitting conjecture. The knot e…

Let $E(K)=S^3-N(K)$ be an exterior of one of the twisted torus knots considered in the paper. The genus-three splitting conjecture. These manifolds possess irreducible yet weakly r…