Distance one lens space fillings and band surgery on the trefoil knot

Abstract

We prove that if the lens space $L(n,1)$ is obtained by a surgery along a knot in the lens space $L(3,1)$ that is distance one from the meridional slope, then $n$ is in $\{-6,\pm 1,\pm 2,3,4,7\}$. This result yields a classification of the coherent and non-coherent band surgeries from the trefoil to $T(2,n)$ torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer $d$-invariants under integral surgery along knots in $L(3,1)$. The classification of band surgeries between the trefoil and torus knots and links is motivated by local reconnection processes in nature, which are modeled as band surgeries. Of particular interest is the study of recombination on circular DNA molecules.

This version accepted for publication in Algebraic & Geometric Topology

References in corpus (6)

• Floer homology and knot complements
• Magnetic reconnection between a solar filament and nearby coronal loops
• The surgery exact triangle in Pin(2)-monopole Floer homology
• Quasi-alternating links with small determinant
• A combinatorial proof of the homology cobordism classification of lens spaces
• Null surgery on knots in L-spaces

Cited by in corpus (3)

• A note on band surgery and the signature of a knot
• Distance one surgeries on the lens space $L(n,1)$
• Studies of distance one surgeries on the lens space $L(p,1)$