Surgery obstructions for knots in integer homology spheres

Yuhui Chen

Surgery obstructions for knots in integer homology spheres

Geometric Topology 2026-07-02 v1

Authors: Yuhui Chen

Abstract

For knot surgery in $S^3$ , Heegaard Floer homology provides an obstruction due to Hom--Karakurt--Lidman. We extend this obstruction to all integer homology spheres $Y$ , for both positive and negative 1/m surgeries. This is used to test infinitely many small Seifert fibered examples and hyperbolic examples. Moreover, we deduce a lower bound on the $b_2(W)$ of smooth cobordism between a pair of integer homology spheres.

Cite

@article{arxiv.2607.02028,
  title  = {Surgery obstructions for knots in integer homology spheres},
  author = {Yuhui Chen},
  journal= {arXiv preprint arXiv:2607.02028},
  year   = {2026}
}