Link cobordism and the intersection of slice discs
Geometric Topology
2018-03-09 v1
Abstract
It is well-known that all 2-knots are slice. Are all 2-links slice? This is an outstanding open question. In this paper we prove the following: For any 2-component 2-link (J,K)in the 4-sphere which bounds the 5-ball B^5, there is an embedded disc 2-disc D^2_J (respectively, D^2_K) in B^5 with the following properties: J (respectively K) bounds D^2_J (respectively, D^2_K). D^2_J and D^2_K intersect transversely. the intersection of D^2_J and D^2_K in D^2_J (respectively, D^2_K) is a trivial 1-knot.
Keywords
Cite
@article{arxiv.1803.02892,
title = {Link cobordism and the intersection of slice discs},
author = {Eiji Ogasa},
journal= {arXiv preprint arXiv:1803.02892},
year = {2018}
}
Comments
7 pages