Studies of distance one surgeries on the lens space L(p, 1)

Abstract

Abstract In this paper, we study distance one surgeries between lens spaces L(p, 1) with p ≥ 5 prime and lens spaces L(n, 1) for $$n \in \mathbb{Z}$$ and band surgeries from T (2, p) to T (2, n). In particular, we prove that L(n, 1) is obtained by a distance one surgery from L(5, 1) only if n=±1, 4, ±5, 6 or ±9, and L(n, 1) is obtained by a distance one surgery from L(7, 1) if and only if n=±1, 3, 6, 7, 8 or 11.