English

On chain link surgeries bounding rational homology balls and $\chi$-slice 3-braid closures

Geometric Topology 2025-04-25 v4

Abstract

We determine which integral surgeries on a large class of circular chain links bound rational homology balls. Our key tool is the lattice-theoretic cubiquity obstruction recently developed by Greene and Owens. We discuss a practical method of computing it, and, as an application, prove that a generalisation of the slice--ribbon conjecture holds for all but one infinite family of quasi-alternating 3-braid links. This extends previous results of Lisca concerning the conjecture for 3-braid knots.

Keywords

Cite

@article{arxiv.2301.06573,
  title  = {On chain link surgeries bounding rational homology balls and $\chi$-slice 3-braid closures},
  author = {Vitalijs Brejevs and Jonathan Simone},
  journal= {arXiv preprint arXiv:2301.06573},
  year   = {2025}
}

Comments

Final version; to appear in Transactions of the AMS. 22 figures, 9 of which are full-page figures