The Alexander Polynomial for Tangles
نویسنده
چکیده
WExpand@expr_D := Expand@expr . w_W ¦ Signature@wD * Sort@wDD; WM@___, 0, ___D = 0; a_ ~WM~ b_ := WExpandADistribute@a ** bD . Ic1_. * w1_WM ** Ic2_. * w2_WM ¦ c1 c2 Join@w1, w2D E; WM@a_, b_, c__D := a ~WM~ WM@b, cD; IM@8<, expr_D := expr; IM@i_, w_WD := If@MemberQ@w, iD, -H-1L^Position@w, iD@@1, 1DD DeleteCases@w, iD, 0D; IM@8is___, i_<, w_WD := IM@8is<, IM@i, wDD; IM@is_List, expr_D := expr . w_W ¦ IM@is, wD
منابع مشابه
A Diagrammatic Alexander Invariant of Tangles
We give a new construction of the one-variable Alexander polynomial of an oriented knot or link, and show that it generalizes to a vector valued invariant of oriented tangles.
متن کاملA Diagrammatic Multivariate Alexander Invariant of Tangles
Recently, Bigelow defined a diagrammatic method for calculating the Alexander polynomial of a knot or link by resolving crossings in a planar algebra. I will present my multivariate version of Bigelow’s calculation. The advantage to my algorithm is that it generalizes to a multivariate tangle invariant up to Reidemeister I. I will conclude with a possible link to subfactor planar algebras from ...
متن کاملar X iv : h ep - t h / 93 09 02 9 v 1 6 S ep 1 99 3 Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial ∗
We discuss multivariable invariants of colored links associated with the N dimensional root of unity representation of the quantum group. The invariants for N > 2 are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When (N, 3) = 1 and N is odd, the invariant does not vanis...
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, ...
متن کاملAffine Birman – Wenzl – Murakami algebras and tangles in the solid torus
The affine Birman–Wenzl–Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009