Topology Seminar: Doubly slice odd pretzel knots

Seminar | October 2 | 4:10-5 p.m. | 3 Evans Hall

 Clayton McDonald, Boston College

 Department of Mathematics

A knot K in $S^3$ is slice if it is the cross section of an embedded 2-sphere in $S^4$, and it is doubly slice if the 2-sphere is unknotted. Although slice knots are very well-studied, doubly slice knots have been given comparatively less attention. We prove that an odd pretzel knot is doubly slice if it has 2n+1 twist parameters consisting of n+1 copies of a and n copies of -a for some odd integer a. Combined with the work of Issa and McCoy, it follows that these are the only doubly slice odd pretzel knots.