Stanislav Jabuka, Tynan Kelly
Published 2017-08-09Version 1
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.
Comments: 31 pages, 17 figures
The chord index, its definitions, applications and generalizations
A survey on knotoids, braidoids and their applications
On homotopy $K3$ surfaces constructed by two knots and their applications
![QR code for arXiv:1708.03000 [math.GT]](http://oss.arxitics.com/images/favicon.svg)