Seifert vs slice genera of knots in twist families and a characterization of braid axes

Kenneth L. Baker, Kimihiko Motegi

Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ a…