The Kauffman Bracket of Virtual Links and the Bollobás–riordan Polynomial
نویسنده
چکیده
We show that the Kauffman bracket [L] of a checkerboard colorable virtual link L is an evaluation of the Bollobás–Riordan polynomial RGL of a ribbon graph associated with L. This result generalizes the celebrated relation between the classical Kauffman bracket and the Tutte polynomial of planar graphs. 2000 Math. Subj. Class. 57M15, 57M27, 05C10, 05C22.
منابع مشابه
Dedicated to Askold Khovanskii on the occasion of his 60th birthday THE KAUFFMAN BRACKET OF VIRTUAL LINKS AND THE BOLLOBÁS-RIORDAN POLYNOMIAL
We show that the Kauffman bracket [L] of a checkerboard colorable virtual link L is an evaluation of the Bollobás-Riordan polynomial RGL of a ribbon graph associated with L. This result generalizes the celebrated relation between the classical Kauffman bracket and the Tutte polynomial of planar graphs.
متن کاملThe Kauffman Bracket and the Bollobás-riordan Polynomial of Ribbon Graphs
For a ribbon graph G we consider an alternating link LG in the 3-manifold G× I represented as the product of the oriented surface G and the unit interval I . We show that the Kauffman bracket [LG] is an evaluation of the recently introduced Bollobás-Riordan polynomial RG. This results generalizes the celebrated relation between Kauffman bracket and Tutte polynomial of planar graphs.
متن کاملNon-orientable quasi-trees for the Bollobás-Riordan polynomial
We extend the quasi-tree expansion of A. Champanerkar, I. Kofman, and N. Stoltzfus to not necessarily orientable ribbon graphs. We study the duality properties of the Bollobás-Riordan polynomial in terms of this expansion. As a corollary, we get a “connected state” expansion of the Kauffman bracket of virtual link diagrams. Our proofs use extensively the partial duality of S. Chmutov.
متن کاملOn two categorifications of the arrow polynomial for virtual knots
Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an integer arrow number calculated from each loop in an oriented state summation for the bracket. The categorifications are based on new gradings associated wi...
متن کاملAn Extended Bracket Polynomial for Virtual Knots and Links
This paper defines a new invariant of virtual knots and flat virtual knots. We study this invariant in two forms: the extended bracket invariant and the arrow polyomial. The extended bracket polynomial takes the form of a sum of virtual graphs with polynomial coefficients. The arrow polynomial is a polynomial with a finite number of variables for any given virtual knot or link. We show how the ...
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 2006