English

The round handle problem

Geometric Topology 2020-07-10 v5

Abstract

We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and the s-cobordism conjecture for 4-manifolds with free fundamental group.

Cite

@article{arxiv.1706.09571,
  title  = {The round handle problem},
  author = {Min Hoon Kim and Mark Powell and Peter Teichner},
  journal= {arXiv preprint arXiv:1706.09571},
  year   = {2020}
}

Comments

8 pages, 3 figures. For version 2, we added a new section that explains the relationship between disc embedding and the surgery and s-cobordism conjectures. Version 3, referee's comments incorporated, to appear in PAMQ

R2 v1 2026-06-22T20:32:55.213Z