English

Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds

Geometric Topology 2024-05-24 v3

Abstract

We point out that recent constructions of inequivalent smooth structures yield a manufacturing procedure of infinite sets of pairwise smoothly non-isotopic nullhomologous 2-tori and spheres inside a myriad of 4-manifolds. The corresponding infinite set consists of topologically isotopic surfaces that topologically bound a handlebody in several instances.

Keywords

Cite

@article{arxiv.2005.11696,
  title  = {Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds},
  author = {Rafael Torres},
  journal= {arXiv preprint arXiv:2005.11696},
  year   = {2024}
}

Comments

Suggestions from a referee are incorporated in v2. Changes include: added Thm B and a discussion of an invariant of Fintushen-Stern to discern the knotted 2-tori, modified proof of Lemma 1, and a new title. v3: To appear Annales de l'Institut Fourier