Meridional surfaces and (1,1)-knots

2006/08/08 by Mario Eudave-Muñoz, Eudave-Munoz, Mario, Enrique Ramı́rez-Losada +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M25 #57N10 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0608205

openalex publication_date 2006/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dehn Surgery on Knots

Related

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• Non-parallel essential surfaces in knot complements
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• Knots with unique minimal genus Seifert surface and depth of knots
• Knot exteriors with all compact surfaces of positive genus essentially embedded