A new algorithm for recognizing the unknot.

Birman, Joan S.; Hirsch, Michael D.

Displaying similar documents to “A new algorithm for recognizing the unknot.”

On iterated torus knots and transversal knots.

Menasco, William W. (2001)

Geometry & Topology

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Legendrian graphs and quasipositive diagrams

Sebastian Baader, Masaharu Ishikawa (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on $S^{3}$ . We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.

Some examples of essential laminations in 3-manifolds

Allen Hatcher (1992)

Annales de l'institut Fourier

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Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.

Levelling an unknotting tunnel.

Goda, Hiroshi, Scharlemann, Martin, Thompson, Abigail (2000)

Geometry & Topology

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On McMullen's and other inequalities for the Thurston norm of link complements.

Dasbach, Oliver T., Mangum, Brian S. (2001)

Algebraic & Geometric Topology

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Shadow world evaluation of the Yang-Mills measure.

Frohman, Charles, Kania-Bartoszynska, Joanna (2004)

Algebraic & Geometric Topology

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Computing triangulations of mapping tori of surface homeomorphisms.

Brinkmann, Peter, Schleimer, Saul (2001)

Experimental Mathematics

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Lefschetz fibrations on compact Stein surfaces.

Akbulut, Selman, Ozbagci, Burak (2001)

Geometry & Topology

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Laminar branched surfaces in 3--manifolds.

Li, Tao (2002)

Geometry & Topology

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On a problem in effective knot theory

Stefano Galatolo (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The following problem is investigated: «Find an elementary function $F (n) : Z \to Z$ such that if $Γ$ is a knot diagram with $n$ crossings and the corresponding knot is trivial, then there is a sequence of Reidemeister moves that proves triviality such that at each step we have less than $F (n)$ crossings». The problem is shown to be equivalent to a problem posed by D. Welsh in [7] and solved by geometrical techniques (normal surfaces).