1. CMB 1999 (vol 42 pp. 257)
|Homotopy of Knots and the Alexander Polynomial |
Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.
Categories:57N10, 57M05, 57M25, 57N65
2. CMB 1997 (vol 40 pp. 370)
|Which $3$-manifolds embed in $\Triod \times I \times I$? |
We classify the compact $3$-manifolds whose boundary is a union of $2$-spheres, and which embed in $T \times I \times I$, where $T$ is a triod and $I$ the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any $3$-manifold in $T \times I \times I$ embeds in a punctured handlebody.
Categories:57N10, 57N35, 57Q35