Knots , Links and Tangles Steven
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منابع مشابه
On Quantum Algebras and Coalgebras, Oriented Quantum Algebras and Coalgebras, Invariants of 1–1 Tangles, Knots and Links
We outline a theory of quantum algebras and coalgebras and their resulting invariants of unoriented 1–1 tangles, knots and links, we outline a theory of oriented quantum algebras and coalgebras and their resulting invariants of oriented 1–1 tangles, knots and links, and we show how these algebras and coalgebras are related. Quasitriangular Hopf algebras are examples of quantum algebras and orie...
متن کاملClassifying and Applying Rational Knots and Rational Tangles
In this survey paper we sketch new combinatorial proofs of the classification of rational tangles and of unoriented and oriented rational knots, using the classification of alternating knots and the calculus of continued fractions. We continue with the classification of achiral and strongly invertible rational links, and we conclude with a description of the relationships among tangles, rationa...
متن کاملRational Structure on Algebraic Tangles and Closed Incompressible Surfaces in the Complements of Algebraically Alternating Knots and Links
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface with boundary in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles....
متن کاملRational Structure on Algebraic Tangles and Closed Incompressible Surfaces in Algebraically Alternating Knots and Links
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles. The slopes an...
متن کاملTangles for Knots and Links
It is often useful to discuss only small “pieces” of a link or a link diagram while disregarding everything else. For example, the Reidemeister moves describe manipulations surrounding at most 3 crossings, and the skein relations for the Jones and Conway polynomials discuss modifications on one crossing at a time. Tangles may be thought of as small pieces or a local pictures of knots or links, ...
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