A Self-Linking Invariant of Virtual Knots
نویسنده
چکیده
In this paper we introduce a new invariant of virtual knots and links that is non-trivial for many virtuals, but is trivial on classical knots and links. The invariant will initially be expressed in terms of a relative of the bracket polynomial [4], and then extracted from this polynomial in terms of its exponents, particularly for the case of knots. The analog of the bracket polynomial will be denoted {K} (with curly brackets) and called the binary bracket polynomial. See Section 3 for the definition and properties of the binary bracket. The key to the combinatorics of this invariant is an interpretation of the state sum in terms of 2-colorings of the associated diagrams.
منابع مشابه
Self-Linking Invariant of Virtual Knots
This paper introduces a self-linking invariant for virtual knots and links, and relates this invariant to a state model called the binary bracket, and to a class of coloring problems for knots and links that include classical coloring problems for cubic graphs. (AMS Subject Classification Number 57M27)
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