Surgeries on torus knots, rational balls, and cabling
[Chirurgies le long de nœuds toriques, boules d’homologie rationnelle et câblages]
Aceto, Paolo1 ; Golla, Marco2 ; Larson, Kyle3 ; G. Lecuona, Ana4
1Laboratoire Paul Painlevé, University of Lille, Lille (France)
2Laboratoire de mathématiques, J. Leray, CNRS, University of Nantes, Nantes (France)
3Department of Mathematics, University of Georgia, Athens, Georgia (U.S.A.)
4School of mathematics, and statistics, University of Glasgow, Glasgow (United Kingdom)
Annales de l'Institut Fourier, Online first, 132 p.

We classify which positive integral surgeries on positive torus knots bound rational homology balls. Additionally, for a given knot $K$ we consider which cables $K_{p,q}$ admit integral surgeries that bound rational homology balls. For such cables, let ${\mathcal{S}}(K)$ be the set of corresponding rational numbers $\frac{q}{p}$. We show that ${\mathcal{S}}(K)$ is bounded for each $K$. Moreover, if $n$-surgery on $K$ bounds a rational homology ball then $n$ is an accumulation point for ${\mathcal{S}}(K)$.

Dans cet article on donne la classification des chirurgies entières positives le long de nœuds toriques positifs qui bordent des boules d’homologie rationnelle. Nous considérons aussi le cas plus général des cables : quels cables $K_{p,q}$ d’un nœud $K$ admettent une chirurgie entière qui borde une boule d’homologie rationnelle ? Pour ces cables, soit ${\mathcal{S}}(K)$ l’ensemble des nombres rationnels $\frac{q}{p}$ correspondants. Nous démontrons que ${\mathcal{S}}(K)$ est borné pour tout $K$ et que, si la $n$-chirurgie le long de $K$ borde une boule d’homologie rationnelle, alors $n$ est un point d’accumulation de ${\mathcal{S}}(K)$.

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DOI : 10.5802/aif.3772
Classification : 57K10, 57K41, 57R65
Keywords: Rational homology balls, Dehn surgery, cabling
Mots-clés : Chirurgie de Dehn, boules d’homologie rationnelle, réseaux intégraux, termes de correction, plongements

Aceto, Paolo  1   ; Golla, Marco  2   ; Larson, Kyle  3   ; G. Lecuona, Ana  4

1 Laboratoire Paul Painlevé, University of Lille, Lille (France)
2 Laboratoire de mathématiques, J. Leray, CNRS, University of Nantes, Nantes (France)
3 Department of Mathematics, University of Georgia, Athens, Georgia (U.S.A.)
4 School of mathematics, and statistics, University of Glasgow, Glasgow (United Kingdom) 
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Aceto, Paolo; Golla, Marco; Larson, Kyle; G. Lecuona, Ana. Surgeries on torus knots, rational balls, and cabling. Annales de l'Institut Fourier, Online first, 132 p.

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