Knot complement problem for L-space ℤHS3

Abstract

In this paper, we look at the knot complement problem for L-space [Formula: see text]-homology spheres. We show that an L-space [Formula: see text]-homology sphere [Formula: see text] cannot be obtained as a non-trivial surgery along a knot [Formula: see text]. As a consequence, we prove that knots in an L-space [Formula: see text]-homology sphere are determined by their complements.