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

2019/06/02 by Zhongtao Wu, Wu, Zhongtao, Jingling Yang +1
Mathematics · #57K10 #57K18 #57K31 #57M12 #57R58 #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1906.00381

openalex publication_date 2019/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, 3, 6, 7, 8 or 11.

Citations

• Floer homology and knot complements
• Lens space surgeries and L-space homology spheres
• Modifications and Cobounding Manifolds

Related

• Distance one surgeries on the lens space L(n,1)
• Surgeries between lens spaces of type L(n,1) and the Heegaard Floer d-invariant
• Surgical distance between lens spaces
• On Legendrian surgeries between lens spaces
• Lens surgeries along the n-twisted Whitehead link