The  Weizmann  Institute  of  Science
Faculty of Mathematics and Computer Science

Seminar in Geometry and Topology

Seminar Room, Room 261, Ziskind Building
on Thursday, January 27, 2011
at 16:00

Note unusual day

Burglind Joricke

will speak on

Analytic knots, satellites and the 4-ball genus

Abstract:
Call a knot in the unit sphere in complex affine $2$-space analytic
(respectively, smoothly analytic) if it bounds a complex curve (respectively,
smooth complex curve) in the complex ball. Let $K$ be a smoothly analytic
knot.  We give a sharp lower bound for the $4$-ball genus of an arbitrary
analytic knot $L$ contained in a small tubular neighborhood of $K$ in terms of
the $4$-ball genus of $K$ and the winding number of $L$ with respect to $K$.
The question is related to branched coverings $p:Y \to X$ of (smoothly bounded)
open Riemann surfaces $X$,  embeddings of $Y$ into a disc bundle over $X$ and
and the braid formed by the related embedding of the boundary of $Y$.

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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
Announcement from: Diana Mandelik   <diana.mandelik@weizmann.ac.il>