Conjugate Generators of Knot and Link Groups
نویسنده
چکیده
This note shows that if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic. This includes the figure-eight knot and Whitehead link groups. Similarly, if two conjugate elements generate the trefoil knot group, then the elements are peripheral.
منابع مشابه
METABELIAN SL(n,C) REPRESENTATIONS OF KNOT GROUPS
We give a classification of irreducible metabelian representations from a knot group into SL(n,C) and GL(n,C). If the homology of the n–fold branched cover of the knot is finite, we show that every irreducible metabelian SL(n,C) representation is conjugate to a unitary representation and that the set of conjugacy classes of such representations is finite. In that case, we give a formula for thi...
متن کاملBraid Groups and Iwahori-hecke Algebras
The braid group Bn is the mapping class group of an n-times punctured disk. The Iwahori-Hecke algebra Hn is a quotient of the braid group algebra of Bn by a quadratic relation in the standard generators. We discuss how to use Hn to define the Jones polynomial of a knot or link. We also summarize the classification of the irreducible representations of Hn. We conclude with some directions for fu...
متن کاملAn algorithm for computing the Seifert matrix of a link from a braid representation
A Seifert surface of a knot or link in S is an oriented surface in S whose boundary coincides with that of the link. A corresponding Seifert matrix has as its entries the linking numbers of a set of homology generators of the surface. Thus a Seifert matrix encodes essential information about the structure of a link and, unsurprisingly, can be used to define powerful invariants, such as the Alex...
متن کاملAlexander Polynomials of Ribbon Links
We give a simple argument to show that every polynomial f(t) ∈ Z[t] such that f(1) = 1 is the Alexander polynomial of some ribbon 2-knot whose group is a 1-relator group, and we extend this result to links. It is well known that every Laurent polynomial f(t) ∈ Λ = Z[t, t] with f(1) = 1 is the Alexander polynomial of some ribbon 2-knot [7]. (See also [1, 2], for the fibred case, and §7H of [11],...
متن کاملCyclically presented groups in which the relators involve at most three generators
Cyclically presented groups Gn(w) in which w involves at most three generators are studied. We classify when such groups have infinite abelianizations and apply this result to the groups Gn(x1x1+kx 1+`). As a further corollary we give sufficient conditions for the natural HNN extension of Gn(w) to be a high-dimensional knot group. By continuing Cavicchioli, Repovš, and Spaggiari’s investigation...
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 2008