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A lower bound on the stable $4$–genus of knots

### Damian Iltgen

Algebraic & Geometric Topology 22 (2022) 2239–2265
##### 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.

##### Keywords
low-dimensional topology, knot theory, stable $4$–genus, concordance group, twist knots
Primary: 57K10