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

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 ∈ 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,