Lecture Event
Analytic knots, satellites and the 4-ball genus
6 Jul 2012, 10:00 – 11:00
Abstract. A satellite of a knot $K$ is a link contained in a tubular neighbourhoof of $K$ (but not in a $3$-ball contained in this neighbourhood), and not isotopic to $K$. In a classical paper Schubert gives a lower bound for the genus of satellites.
Consider a knot or link in the unit sphere in $\mathbb C2$. Call it analytic (respectively, smoothly analytic) if it bounds a complex curve (respectively, a smooth complex curve) in the complex ball.
Let $K$ be a smoothly analytic knot. For analytic satellite links
contained in a sufficiently small tubular neighbourhood of $K$ there is a (sharp) lower bound of the $4$-ball genus (but not of the genus).
Moreover, these links can be completely described. The problem is related to branched coverings and braided surfaces.
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