A note on the concordance $\mathbb{Z}$-genus
Geometric Topology
2021-03-03 v1
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.
Cite
@article{arxiv.2103.01726,
title = {A note on the concordance $\mathbb{Z}$-genus},
author = {Allison N. Miller and JungHwan Park},
journal= {arXiv preprint arXiv:2103.01726},
year = {2021}
}
Comments
7 pages