A lower bound on the stable 4-genus of knots

Abstract

We present a lower bound on the stable $4$-genus of a knot based on Casson-Gordon $\tau$-signatures. We compute the lower bound for an infinite family of knots, the twist knots, and show that a twist knot is torsion in the knot concordance group if and only if it has vanishing stable $4$-genus.

24 pages, 4 figures, comments welcome. V3: Corrected the statement of Proposition 4 and 6, and Theorem 7 (main theorem). Applications to twist knots remain valid and unchanged