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2019 Distance one lens space fillings and band surgery on the trefoil knot
Tye Lidman, Allison H Moore, Mariel Vazquez
Algebr. Geom. Topol. 19(5): 2439-2484 (2019). DOI: 10.2140/agt.2019.19.2439

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,±1,±2,3,4,7}. This result yields a classification of the coherent and noncoherent 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.

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Tye Lidman. Allison H Moore. Mariel Vazquez. "Distance one lens space fillings and band surgery on the trefoil knot." Algebr. Geom. Topol. 19 (5) 2439 - 2484, 2019. https://doi.org/10.2140/agt.2019.19.2439

Information

Received: 19 December 2017; Revised: 12 August 2018; Accepted: 16 October 2018; Published: 2019
First available in Project Euclid: 26 October 2019

zbMATH: 07142610
MathSciNet: MR4023320
Digital Object Identifier: 10.2140/agt.2019.19.2439

Subjects:
Primary: 57M25, 57M27, 57R58
Secondary: 92E10

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 5 • 2019
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