Banff Workshop Proposal: Knot Theory and Virtual Knot Theory
نویسندگان
چکیده
1.
منابع مشابه
From 3-moves to Lagrangian tangles and cubic skein modules
We present an expanded version of four talks describing recent developments in Knot Theory to which the author contributed. We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups. The method of Burnside groups of links was discovered and developed only half a year after the last talk ...
متن کاملVirtual Knots and Links
This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: We prove, using a 3-dimensional topology approach that if a connected sum of two virtual knots K1 and K2 is trivial, then so are both K1 and K2. We establish an algorithm, using Haken-Matveev technique, for recognizing...
متن کاملOn a Generalization of Alexander Polynomial for Long Virtual Knots
We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by ζ meaning an analogy with ζ-polynomial for virtual links. A degree of ζ-polynomial estimates a virtual crossing number. We describe some application of ζpolynomial for the study of minimal long virtual diagrams with respect number of virtual crossings. Virtual knot th...
متن کاملCrowell’s Derived Group and Twisted Polynomials
The derived group of a permutation representation, introduced by R.H. Crowell, unites many notions of knot theory. We survey Crowell’s construction, and offer new applications. The twisted Alexander group of a knot is defined. Using it, we obtain twisted Alexander modules and polynomials. Also, we extend a well-known theorem of Neuwirth and Stallings giving necessary and sufficient conditions f...
متن کاملRelative Tutte Polynomials for Coloured Graphs and Virtual Knot Theory
We introduce the concept of a relative Tutte polynomial. We show that the relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (hence the Jones polynomial) of a virt...
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تاریخ انتشار 2014