On the Jones polynomials of checkerboard colorable virtual knots
نویسنده
چکیده
In this paper we study the Jones polynomials of virtual links and abstract links. It is proved that a certain property of the Jones polynomials of classical links is valid for virtual links which admit checkerboard colorings.
منابع مشابه
Relative 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...
متن کاملGuts of Surfaces and the Colored Jones Polynomial
This work initiates a systematic study of relations between quantum and geometric knot invariants. Under mild diagrammatic hypotheses that arise naturally in the study of knot polynomial invariants (A– or B–adequacy), we derive direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. We prove that the grow...
متن کاملTwisted Link Theory
We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation I -bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the virtual knots introduced by L. Kauffman, and the projective links introduced by Yu. Drobotukhina. We show that these links have unique minimal genus three-manifolds...
متن کاملNonalternating knots and Jones polynomials
We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones polynomials.
متن کاملSlopes and Colored Jones Polynomials of Adequate Knots
Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We verify this conjecture for adequate knots, a class that vastly generalizes that of alternating knots.
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