Alexander Groups and Virtual Links Daniel
نویسنده
چکیده
The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.
منابع مشابه
Alexander Groups and Virtual Links
The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.
متن کاملOn Alexander-Conway Polynomials for Virtual Knots and Links
A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauffman, and Saleur, is defined and its properties are investigated. Examples are given that the invariant can detect chirality and even non-invertibility of virtual knots and links. Furthermore, it is shown that the polynomial satisfies a Conway-type skein relation – in cont...
متن کاملOn Alexander-conway Polynomials for Virtual Knots and Links
A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauuman, and Saleur, is deened and its properties are investigated. Examples are given that the invariant can detect chirality and even non-invertibility of virtual knots and links. Furthermore, it is shown that the polynomial satisses a Conway-type skein relation { in contras...
متن کاملBi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links
This paper discusses the construction of a generalized Alexander polynomial for virtual knots and links, and the reformulation of this invariant as a quantum link invariant. We then introduce the concept of a bi-oriented quantum algebra which provides an algebraic context for this structure.
متن کاملAn Invariant for Open Virtual Strings
Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice open virtual string that is not ribbon. Definitions are extended to open n-strings.
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 2001