On continuous families of geometric Seifert conemanifold structures


Autoria(s): Lozano Imízcoz, María Teresa; Montesinos Amilibia, José María
Data(s)

2016

Resumo

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.

Formato

application/pdf

Identificador

http://eprints.ucm.es/39920/1/Montesinos77.pdf

Idioma(s)

en

Publicador

World Scientific Publishing Co. Pte Ltd

Relação

http://eprints.ucm.es/39920/

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

http://dx.doi.org/10.1142/S0218216516500838

MTM2013-45710-c2-1-p

MTM2015-63612-P

Direitos

info:eu-repo/semantics/openAccess

Palavras-Chave #Topología
Tipo

info:eu-repo/semantics/article

PeerReviewed