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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Meridional surfaces and $ (1,1)$-knots


Authors: Mario Eudave-Muñoz and Enrique Ramírez-Losada
Journal: Trans. Amer. Math. Soc. 361 (2009), 671-696
MSC (2000): Primary 57M25, 57N10
Published electronically: September 9, 2008
MathSciNet review: 2452820
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Abstract: We determine all $ (1,1)$-knots which admit an essential meridional surface, namely, we give a construction which produces $ (1,1)$-knots having essential meridional surfaces, and show that if a $ (1,1)$-knot admits an essential meridional surface, then it comes from the given construction.


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Mario Eudave-Muñoz
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México D.F., Mexico
Email: mario@matem.unam.mx

Enrique Ramírez-Losada
Affiliation: Centro de Investigación en Matemáticas, Apdo. Postal 402, 36000 Guanajuato, Gto., Mexico
Email: kikis@cimat.mx

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04385-7
PII: S 0002-9947(08)04385-7
Keywords: $(1,1)$-knot, essential meridional surface
Received by editor(s): February 10, 2005
Received by editor(s) in revised form: August 7, 2006
Published electronically: September 9, 2008
Article copyright: © Copyright 2008 American Mathematical Society