English

Exotically knotted 2-spheres and the fundamental groups of their complements

Geometric Topology 2025-12-23 v2

Abstract

We show that for any finitely presented group GG, there is a simply connected closed 4-manifold containing an infinite family of topologically isotopic but smoothly inequivalent 2-links whose 2-link group is GG. We also show that, if GG satisfies the necessary topological conditions, these 2-links have nullhomotopic components.

Keywords

Cite

@article{arxiv.2406.07093,
  title  = {Exotically knotted 2-spheres and the fundamental groups of their complements},
  author = {Younes Benyahia},
  journal= {arXiv preprint arXiv:2406.07093},
  year   = {2025}
}

Comments

11 pages, 3 figures. Lemma 5.1 added + referees' suggestions. To appear in Proc. Amer. Math. Soc