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Representing knots by filling Dehn spheres

Álvaro Lozano-Rojo

Centro Universitario de la Defensa Zaragoza, AGM. Ctra. de Huesca s/n, 50090 Zaragoza, Spain

Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Spain

E-mail Address: alozano@unizar.es

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and

Rubén Vigara

Centro Universitario de la Defensa Zaragoza, AGM. Ctra. de Huesca s/n, 50090 Zaragoza, Spain

Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Spain

E-mail Address: rvigara@unizar.es

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https://doi.org/10.1142/S0218216516500188Cited by:1 (Source: Crossref)

Abstract

We prove that any knot or link in any $3$ -manifold can be nicely decomposed (split) by a filling Dehn sphere. This has interesting consequences in the study of branched coverings over knots and links. We give an algorithm for computing Johansson diagrams of filling Dehn surfaces out from coverings of $3$ -manifolds branched over knots or links.

Keywords:

AMSC: 57N10, 57M25, 57N35

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