English

Knot Complement Problem for L-space $\mathbb{Z} HS^3$

Geometric Topology 2022-11-18 v5

Abstract

In this paper we look at the knot complement problem for L-space Z\mathbb{Z}-homology spheres. We show that an L-space Z\mathbb{Z}-homology sphere YY cannot be obtained as a non-trivial surgery along a knot KYK\subset Y. As a consequence, we prove that knots in an L-space Z\mathbb{Z}-homology sphere are determined by their complements.

Keywords

Cite

@article{arxiv.1505.00239,
  title  = {Knot Complement Problem for L-space $\mathbb{Z} HS^3$},
  author = {Huygens C. Ravelomanana},
  journal= {arXiv preprint arXiv:1505.00239},
  year   = {2022}
}

Comments

The comment after Theorem 1.2 has been corrected, the adjective irreducible has been added. "The Poincare sphere {\Sigma}(2, 3, 5) is the only known irreducible L-space Z-homology sphere apart from S^3."

R2 v1 2026-06-22T09:26:44.871Z