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On continuous families of geometric Seifert conemanifold structures

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Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2016) On continuous families of geometric Seifert conemanifold structures. Journal of Knot Theory and its Ramifications . ISSN 02182165

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0218216516500838?src=recsys




Abstract

In this paper, dedicated to Prof. Lou Kauffman, we determine the Thurston’s geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space (Formula presented.) and no more than three exceptional fibers, whose singular set, composed by fibers, has at most three components which can include exceptional or general fibers (the total number of exceptional and singular fibers is less than or equal to three). We also give the method to obtain the holonomy of that structure. We apply these results to three families of Seifert manifolds, namely, spherical, Nil manifolds and manifolds obtained by Dehn surgery on a torus knot (Formula presented.). As a consequence we generalize to all torus knots the results obtained in [Geometric conemanifolds structures on (Formula presented.), the result of (Formula presented.) surgery in the left-handed trefoil knot (Formula presented.), J. Knot Theory Ramifications 24(12) (2015), Article ID: 1550057, 38pp., doi: 10.1142/S0218216515500571] for the case of the left handle trefoil knot. We associate a plot to each torus knot for the different geometries, in the spirit of Thurston.


Item Type:Article
Uncontrolled Keywords:Conemanifold; Dehn surgery; Seifert manifold; torus knot
Subjects:Sciences > Mathematics > Topology
ID Code:39920
Deposited On:05 Nov 2016 16:52
Last Modified:12 Dec 2018 15:12

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