Bipartite knots

Sergei Duzhin; Mikhail Shkolnikov

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Displaying similar documents to “Bipartite knots”

Minimal surface representations of virtual knots and links.

Dye, H.A., Kauffman, Louis H. (2005)

Algebraic & Geometric Topology

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Computations of the Ozsvath-Szabo knot concordance invariant.

Livingston, Charles (2004)

Geometry & Topology

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Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

Seiichi Kamada (2001)

Fundamenta Mathematicae

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A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need...

Crosscaps and knots.

Clark, Bradd Evans (1978)

International Journal of Mathematics and Mathematical Sciences

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Splitting the concordance group of algebraically slice knots.

Livingston, Charles (2003)

Geometry & Topology

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Small Seifert-fibered Dehn surgery on hyperbolic knots.

Dean, John C. (2003)

Algebraic & Geometric Topology

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Virtual Legendrian isotopy

Vladimir Chernov, Rustam Sadykov (2016)

Fundamenta Mathematicae

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An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. In contrast to Legendrian knots, virtual Legendrian knots...

An operator invariant for handlebody-knots

Kai Ishihara, Atsushi Ishii (2012)

Fundamenta Mathematicae

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A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.

The concordance genus of knots.

Livingston, Charles (2004)

Algebraic & Geometric Topology

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Bounds for the Thurston-Bennequin number from Floer homology.

Plamenevskaya, Olga (2004)

Algebraic & Geometric Topology

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Mp-small summands increase knot width.

Hendricks, Jacob (2004)

Algebraic & Geometric Topology

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New topologically slice knots.

Friedl, Stefan, Teichner, Peter (2005)

Geometry & Topology

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Quasipositivity and new knot invariants.

Lee Rudolph (1989)

Revista Matemática de la Universidad Complutense de Madrid

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This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.

Thin presentation of knots and lens spaces.

Deruelle, A., Matignon, D. (2003)

Algebraic & Geometric Topology

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The slicing number of a knot.

Livingston, Charles (2002)

Algebraic & Geometric Topology

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Applications of topology to DNA

Isabel Darcy, De Sumners (1998)

Banach Center Publications

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The following is an expository article meant to give a simplified introduction to applications of topology to DNA.