Quasipositivity as an obstruction to sliceness
| dc.creator | Rudolph, Lee | |
| dc.date | 1993-07-01 | |
| dc.date | 2000-03-24 | |
| dc.date.accessioned | 2026-07-07T09:04:41Z | |
| dc.date.available | 2026-07-07T09:04:41Z | |
| dc.description | For an oriented link $L \subset S^3 = \Bd\!D^4$, let $χ_s(L)$ be the greatest Euler characteristic $χ(F)$ of an oriented 2-manifold $F$ (without closed components) smoothly embedded in $D^4$ with boundary $L$. A knot $K$ is {\it slice} if $χ_s(K)=1$. Realize $D^4$ in $\C^2$ as $\{(z,w):|z|^2+|w|^2\le1\}$. It has been conjectured that, if $V$ is a nonsingular complex plane curve transverse to $S^3$, then $χ_s(V\cap S^3)=χ(V\cap D^4)$. Kronheimer and Mrowka have proved this conjecture in the case that $V\cap D^4$ is the Milnor fiber of a singularity. I explain how this seemingly special case implies both the general case and the ``slice-Bennequin inequality'' for braids. As applications, I show that various knots are not slice (e.g., pretzel knots like $\Pscr(-3,5,7)$; all knots obtained from a positive trefoil $O\{2,3\}$ by iterated untwisted positive doubling). As a sidelight, I give an optimal counterexample to the ``topologically locally-flat Thom conjecture''. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/9307233 | |
| dc.identifier | http://arxiv.org/abs/math/9307233 | |
| dc.identifier | Bull. Amer. Math. Soc. (N.S.) 29 (1993) 51-59 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149468 | |
| dc.subject | Geometric Topology | |
| dc.title | Quasipositivity as an obstruction to sliceness | |
| dc.type | text |