On the slice-ribbon conjecture for Montesinos knots

Lecuona, A. G. (2012) On the slice-ribbon conjecture for Montesinos knots. Transactions of the American Mathematical Society, 364(1), pp. 233-285. (doi:10.1090/S0002-9947-2011-05385-7)

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Abstract

We establish the slice-ribbon conjecture for a family 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 S2 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 #vertices < −1. The Seifert spaces which bound these 4-dimensional plumbing manifolds are the double covers of S3 branched along the Montesinos knots in the family P.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Lecuona, Dr Ana
Authors: Lecuona, A. G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Transactions of the American Mathematical Society
Publisher:American Mathematical Society
ISSN:0002-9947
ISSN (Online):1088-6850

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