Extending Quotients of Knot Groups over Surfaces in $B^4$

Alexandra Kjuchukova, Kent E. Orr

Let $K\subseteq S^3$ be a knot with exterior $E_K$, and denote by $\ddot{I}:\ddot{I}{€}_1(E_K)\twoheadrightarrow G$ a quotient of its group. We give a sharp obstruction to the existence of…