English

Triple linking and rational homology cobordism

Geometric Topology 2026-02-11 v2

Abstract

If a rational homology 3-sphere MM bounds a rational homology 4-ball WW, then the kernel of the inclusion-induced homomorphism H1(M;Z)H1(W;Z)H_1(M;\mathbb{Z})\to H_1(W;\mathbb{Z}) is a Lagrangian for the Q/Z\mathbb{Q}/\mathbb{Z}-valued torsion linking form λ2\lambda_2 on H1(M;Z)H_1(M;\mathbb{Z}). In this short paper, we prove that the Freedman-Krushkal triple torsion linking form λ3\lambda_3 (arXiv:2506.11941v3) vanishes on this Lagrangian under the assumption that H2(W;Z)=0H_2(W;\mathbb{Z})=0. We then pose several questions about topological rational homology cobordism.

Keywords

Cite

@article{arxiv.2511.03818,
  title  = {Triple linking and rational homology cobordism},
  author = {Ryan Stees},
  journal= {arXiv preprint arXiv:2511.03818},
  year   = {2026}
}

Comments

7 pages, 1 figure. From v1, only typographical changes have been made