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 $$n \in \mathbb{Z}$$ 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.

On pseudo-horizontal surfaces and $\mathbb{Z}_2$-Thurston norms in small Seifert $3$-manifolds

“…Now (α 1 , β 1 , γ 1 , δ 1 ) = (3, −1, −2, 1), (α 2 , β 2 , γ 2 , δ 2 ) = (4, 1, 3, 1), and (α 3 , β 3 , γ 3 , δ 3 ) = (2n, 1, 2n − 1, 1). Let (λ 1 , µ 1 ) = (3, −1), (λ 2 , µ 2 ) = (4, 1), and (λ 3 , µ 3 ) = (12,1). Then λ = 12, the genus of the pseudo-horizontal surface is…”

“…It uses Heegaard Floer homology and calculates the correction term. Using the algorithm in [12] and an online program given by [7], we try to compute the lower bound of the Z 2 -Thurston norm for the previous examples when the parameters m, n are not too large. We find the results in our examples meet the lower bounds of the Z 2 -Thurston norms.…”