KNOTS IN HOMOLOGY LENS SPACES DETERMINED BY THEIR COMPLEMENTS

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H-1 (M; Z) congruent to Z(p) and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H-1 (L(p, q)).