Covers of S^3 bounding covers of B^4

Abstract: Let $G$ be a group, $K$ a knot and $\rho$ a surjective homomorphism $\pi_1(S^3 \backslash K) \to G$. When does a branched cover of $S^3$ determined by $\rho$ extend over $B^4$, with a smooth branching locus $F$? Previously, the answer was only known under quite strong assumptions, e.g. when K is slice and G a dihedral group. I will define a new invariant which detects the existence of such an extension for all knots and all metabelian groups. I will give examples of computing the obstruction and constructing the desired surface $F$. Joint work with Kent Orr.

Mathematics

Audience: researchers in the discipline

Regensburg low-dimensional geometry and topology seminar