The non-orientable 4-genus for knots with 8 or 9 crossings
Geometric Topology
2020-09-09 v3
Abstract
The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the given knot. We compute the non-orientable 4-genus for all knots with crossing number 8 or 9. As applications we prove a conjecture of Murakami's and Yasuhara's, and give a new lower bound for the slicing number of knot.
Keywords
Cite
@article{arxiv.1708.03000,
title = {The non-orientable 4-genus for knots with 8 or 9 crossings},
author = {Stanislav Jabuka and Tynan Kelly},
journal= {arXiv preprint arXiv:1708.03000},
year = {2020}
}
Comments
Fixed two values of $\gamma_4$ arising from a typographical error. Updated references. Added Journal Ref