A note on cabled slice knots and reducible surgeries

DOI10.1307/MMJ/1490639817zbMATH Open1370.57004arXiv1507.04562OpenAlexW3105447471MaRDI QIDQ2363551

Jeffrey Meier

Publication date: 20 July 2017

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Abstract: We consider the question of when a slice knot admits a reducible Dehn surgery. By analyzing the correction terms associated to such a surgery, we show that slice knots cannot admit surgeries with more than two summands. We also give a necessary Heegaard Floer theoretic condition for a positive cable of a knot to be slice.

Full work available at URL: https://arxiv.org/abs/1507.04562

zbMATH Keywords

Dehn surgeryslice knotHeegard Floer homologyirreducible 3-manifoldcabled knot

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Surgery and handlebodies (57R65)

Related Items (4)

A note on cabling and \(L\)-space surgeries ⋮ A surgery formula for knot Floer homology ⋮ THE HALF-TWISTED SPLICE OPERATION ON REDUCED KNOT PROJECTIONS ⋮ Producing reducible 3-manifolds by surgery on a knot

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