On the slice-ribbon conjecture for Montesinos knots

G. Lecuona, Ana

doi:10.1090/S0002-9947-2011-05385-7

On the slice-ribbon conjecture for Montesinos knots
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by Ana G. Lecuona

Trans. Amer. Math. Soc. 364 (2012), 233-285

DOI: https://doi.org/10.1090/S0002-9947-2011-05385-7

Published electronically: July 20, 2011

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Abstract:

We establish the slice-ribbon conjecture for a family $\mathscr {P}$ of Montesinos knots by means of Donaldson’s theorem on the intersection forms of definite $4$-manifolds. The $4$-manifolds that we consider are obtained by plumbing disc bundles over $S^2$ according to a star-shaped negative-weighted graph with $3$ legs such that: i) the central vertex has weight less than or equal to $- 3$; ii) $- \mbox {total weight} - 3 \# \mbox {vertices} <-1$. The Seifert spaces which bound these $4$-dimensional plumbing manifolds are the double covers of $S^3$ branched along the Montesinos knots in the family $\mathscr {P}$.

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