Crosscaps and knots.

Clark, Bradd Evans

Displaying similar documents to “Crosscaps and knots.”

Minimal surface representations of virtual knots and links.

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

Algebraic & Geometric 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...

Computations of the Ozsvath-Szabo knot concordance invariant.

Livingston, Charles (2004)

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).

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.