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 -homology spheres. We show that an L-space -homology sphere cannot be obtained as a non-trivial surgery along a knot . As a consequence, we prove that knots in an L-space -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."