On the slice genus of generalized algebraic knots

Abstract

We give examples of a linear combination of algebraic knots and their mirrors that are algebraically slice, but whose topological and smooth four-genus is two. Our examples generalize an example of non-slice algebraically slice linear combination of iterated torus knots obtained by Hedden, Kirk and Livingston. Our main tool is a genus bound from Casson–Gordon theory and a cabling formula that allows us to compute effectively these invariants.