Displaying similar documents to “A new proof of Markov's braid theorem”

Reidemeister-type moves for surfaces in four-dimensional space

Dennis Roseman (1998)

Banach Center Publications

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We consider smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in ℝ n + 2 (or S n + 2 ), for the cases n=2 or n=3. In a previous paper we have generalized the notion of the Reidemeister moves of classical knot theory. In this paper we examine in more detail the above mentioned dimensions. Examples are given; in particular we examine projections of twist-spun knots. Knot moves are given which demonstrate the triviality of the 1-twist spun trefoil. Another application...

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.

Climbing a Legendrian mountain range without stabilization

Douglas J. LaFountain, William W. Menasco (2014)

Banach Center Publications

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We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary...

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.