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

Abstract

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

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

References in corpus (3)

• Knot Floer homology detects fibred knots
• Lens space surgeries and L-space homology spheres
• Heegaard Floer homology and knots determined by their complements

Cited by in corpus (2)

• The Legendrian knot complement problem
• Ribbon disks with the same exterior