Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Are there stably irreducible surface-knots in $S^4$ of every (including non-orientable) genus? Livingston gave examples of stably irreducible, orientable knotted surfaces of arbitrary genus in $S^4$. In the non-orientable case, the Kinoshita conjecture posits that all projective planes in $S^4$ are reducible. Although, Yoshikawa gave infinitely many irreducible Klein bottles in $S^4$ where after taking connected sums give irreducible, non-orientable surfaces of arbitrary even genus. His method cannot detect if the surfaces are stably irreducible, but I will use the symmetric quandle cocycle invariant to show that there exist stably irreducible surface-knots of arbitrary even genus.

Pizza at 11:50am