Knots and Links

By D. Rolfsen. 2003

2,557 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Language and Linguistics

View Paper: https://www.semanticscholar.org/paper/5d962ff7f58d35219a479a8d7f456436c50f9de4

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In Biomedical Engineering

In Language and Linguistics

Citations in the corpus

Small dilatation mapping classes coming from the simplest hyperbolic braid (2009, methodology): “The Alexander polynomial for L is given by ∆L(x, u) = u 2 − u(1− x− x−1) + 1 (3) (see Rolfsen’s table [24]), and the Teichmüller polynomial is given by”
A Survey of Classical Knot Concordance (2003, background): “General references concerning concordance which were of great benefit to me as I learned the subject include [37, 96].”
Representations of Knot Groups and Twisted Alexander Polynomials (2001, background): “Let us first recall the definition of the Alexander module of a knot K (see [10]).”
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation (2008, methodology): “Then a standard calculation using the Seifert form (see [36]) shows that H1(B3) = Z25 ⊕Z25.”
THE CONJUGACY PROBLEM IN SMALL GAUSSIAN GROUPS (2001, background): “The braid monoids of the complex reflection groups G7, G11, G12, G13, G15, G19 and G22 given in [4], the braid monoids of Birman-Ko-Lee [2], several of monoids of torus knots or links [16], and several of braid monoids of Sergiescu [17] are also small Gaussian monoids.”
A Proof of the Finite Filling Conjecture (2001, background): “Our references for the basic notions, terminology and notation relating to the topology of 3-manifolds are [19] and [20], for knot theory [29], for algebraic geometry [30], and for the SL(2,C)-character varieties of 3-manifolds [12].”
The Superpolynomial for Knot Homologies (2005, background): “In particular, the trefoil knot 31 in the standard tables [Rolfsen 76, BarNatan 05c] is exactly T2,3 with our conventions.”
Braids: A Survey (2004, methodology): “The Yamada-Vogel algorithm draws on Seifert’s well-known algorithm for using a diagram of an oriented knot or link K to construct a Seifert surface for K (see [123] or [101], e.”
A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods (2009, background): “A number of invariants has been proposed which include basic numerical, polynomial and finite type invariants (or Vassiliev invariants) [40, 41, 43], but none of these has been proven to distinguish between all knots or links.”
A concordance invariant from the Floer homology of double branched covers (2005, methodology): “For the convenience of the reader, the two ten crossing knots are also shown in Rolfsen’s notation [35].”
The Thurston norm, fibered manifolds and twisted Alexander polynomials (2005, methodology): “rossing links. McMullen [Mc02] determined the Thurston norm for all links with 9 or fewer crossings and with three or fewer components, except for 93 21,9 2 41,9 2 50 and 93 15 (here we use Rolfsen’s [Rol90] notation). For the link 9 3 21 the multivariable Alexander polynomial vanishes, and also all”