Surgeries between lens spaces of type L(n,1) and the Heegaard Floer d-invariant

2025/04/03 by Zhongtao Wu, Wu, Zhongtao, Jingling Yang +1
Mathematics · #57K10 #57K18 #57K31 #57M12 #57R58 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2504.02325

openalex publication_date 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a d-invariant surgery formula for L-space knots that provides an effective tool for studying surgeries between lens spaces. Using this formula, we classify distance one surgeries between lens spaces of the form L(n,1). This classification has direct applications to band surgeries between torus links T(2,n), with connections to DNA topology. In particular, we show that chirally cosmetic banding of torus links can possibly occur only when n=1,5,9 or 10.

Related

• Distance one surgeries on the lens space L(n,1)
• The lens space realization problem
• Lens space surgeries & primitive/Seifert type constructions
• L-space surgeries, genus bounds, and the cabling conjecture
• An explicit description of (1,1) L-space knots, and non-left-orderable surgeries