On the slice genus of generalized algebraic knots

Maria Marchwicka; Wojciech Politarczyk

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arXiv · 2107.11299

On the slice genus of generalized algebraic knots

Maria Marchwicka·Wojciech Politarczyk

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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 invariants and a cabling formula that allows us to compute effectively these invariants.

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BibTeX RIS

Maria Marchwicka, Wojciech Politarczyk. 2021-07-23. On the slice genus of generalized algebraic knots. https://arxiv.org/abs/2107.11299

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