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Geometry and Topology Seminar

Friday, February 23, 2018
3:00pm to 4:00pm
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Building 15, Room 104
A Characterization of Braid Axes
Ken Baker, Department of Mathematics, University of Miami ,
Let $\{K_n\}$ be the family of knots obtained by twisting a knot $K$ in $S^3$ along an unknot $c$. When the winding number of $K$ about $c$ is non-zero, we show the ratio $g(K_n)/g_4(K_n)$ limits to $1$ if and only if the winding and wrapping numbers of $K$ about $c$ are equal. When equal, this leads to a description of minimal genus Seifert surfaces of $K_n$ for $|n| \gg 0$ and eventually to a characterization of when $c$ is a braid axis for $K$. This is joint work with Kimihiko Motegi that builds upon joint work with Scott Taylor about the behavior of the Thurston norm under Dehn filling.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].