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On the slice-ribbon conjecture for Montesinos knots


Author: Ana G. Lecuona
Journal: Trans. Amer. Math. Soc. 364 (2012), 233-285
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9947-2011-05385-7
Published electronically: July 20, 2011
MathSciNet review: 2833583
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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)  $ -$   total weight$ - 3 \char93 $   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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Additional Information

Ana G. Lecuona
Affiliation: Dipartimento di Matematica, Università di Pisa, 56127 Pisa, Italy
Address at time of publication: UMPA-ENS Lyon, 46 allée d’Italie, 69364 Lyon, France
Email: lecuona@mail.dm.unipi.it, ana.garcia_lecuona@ens-lyon.fr

DOI: https://doi.org/10.1090/S0002-9947-2011-05385-7
Keywords: Montesinos links, slice-ribbon conjecture, rational homology balls
Received by editor(s): November 15, 2009
Received by editor(s) in revised form: May 26, 2010
Published electronically: July 20, 2011
Additional Notes: The author wss supported by Spanish GAAR MTM2008-00272/MTM and Proyecto Santander Complutense PR34/07-15813
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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