A note on the concordance $\mathbb{Z}$-genus

Allison N. Miller; JungHwan Park

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arXiv · 2103.01726

A note on the concordance $\mathbb{Z}$-genus

Allison N. Miller·JungHwan Park

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Abstract

We show that the difference between the topological 4-genus of a knot and the minimal genus of a surface bounded by that knot that can be decomposed into a smooth concordance followed by an algebraically simple locally flat surface can be arbitrarily large. This extends work of Hedden-Livingston-Ruberman showing that there are topologically slice knots which are not smoothly concordant to any knot with trivial Alexander polynomial.

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Allison N. Miller, JungHwan Park. 2021-03-02. A note on the concordance $\mathbb{Z}$-genus. https://arxiv.org/abs/2103.01726

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