Lescop invariants of both the Brieskorn–Hamm manifolds and 3-manifolds obtained by Dehn surgeries on knots

Let [Formula: see text] and [Formula: see text] be pairwise coprime with [Formula: see text] and [Formula: see text]. Let the Brieskorn–Hamm manifold be a homology lens space and the order its the first homology group is [Formula: see text]. We classify the Brieskorn–Hamm manifold and the resulting [Formula: see text]-manifold of [Formula: see text]-surgery along a knot [Formula: see text] in [Formula: see text] by using the Lescop invariant.