Knot polynomials and generalized mutation
نویسندگان
چکیده
منابع مشابه
0 M ay 2 00 4 KNOT POLYNOMIALS AND GENERALIZED MUTATION
The motivation for this work was to construct a nontrivial knot with trivial Jones polynomial. Although that open problem has not yielded, the methods are useful for other problems in the theory of knot polynomials. The subject of the present paper is a generalization of Conway's mutation of knots and links. Instead of flipping a 2-strand tangle, one flips a many-string tangle to produce a gene...
متن کاملKnot Polynomials and Knot Homologies
This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories, and give some examples which illustrate a somewhat mysterious correspondence between them.
متن کاملMetabelian representations , twisted Alexander polynomials , knot slicing , and mutation
Given a knot complement X and its p-fold cyclic cover X p → X , we identify twisted polynomials associated to GL1 ( F[t±1] ) representations ofπ1(X p) with twisted polynomials associated to related GL p ( F[t±1] ) representations of π1(X) which factor through metabelian representations. This provides a simpler and faster algorithm to compute these polynomials, allowing us to prove that 16 (of 1...
متن کاملKnot polynomials via one parameter knot theory
We construct new knot polynomials. Let V be the standard solid torus in 3-space and let pr be its standard projection onto an annulus. LetM be the space of all smooth oriented knots in V such that the restriction of pr is an immersion (e.g. regular diagrams of a classical knot in the complement of its meridian). There is a canonical one dimensional homology class for each connected component of...
متن کاملSeifert circles and knot polynomials
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case. Notation. In a diagram D for an oriented knot, write ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1989
ISSN: 0166-8641
DOI: 10.1016/0166-8641(89)90031-x