Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant
نویسندگان
چکیده
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. We generalize this invariant to virtual link diagrams. This result is used to demonstrate that there are virtual knot diagrams with a non-trivial Witten-Reshetikhin-Turaev invariant and trivial fundamental group.
منابع مشابه
On the integrality of Witten-Reshetikhin-Turaev 3-manifold invariants
We prove that the SU.(2) Witten-Reshetikhin-Turaev invariant of any 3-manifold with any colored link inside at any root of unity is an algebraic integer. As a byproduct, we get a new proof of the integrality of the SO.(3) Witten-Reshetikhin-Turaev invariant for any 3-manifold with any colored link inside at any root of unity of odd order. DOI: https://doi.org/10.4171/QT/48 Posted at the Zurich ...
متن کاملOn the quantum sl2 invariants of knots and integral homology spheres
We will announce some results on the values of quantum sl2 invariants of knots and integral homology spheres. Lawrence’s universal sl2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl2 . This implies an integrality result on the colored Jones polynomials of a knot. We define an invariant of integral homolo...
متن کاملLickorish Invariant and Quantum Osp(1|2)
Since Jones’ seminal work[1], the theories of knots and 3 manifolds have made dramatical progress ( See [2] for a review). By now several approachs are available for constructing the so called quantum invariants of 3 manifolds, notably, the quantum field theoretical approach[3], the quantum group approach[4], Lickorish’s recoupling theory[5], the 6j symbol method of Turaev Viro[6], and the conf...
متن کاملUnified Quantum Invariants and Their Refinements for Homology 3–spheres with 2–torsion
For every rational homology 3–sphere with H1(M, Z) = (Z/2Z) n we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten–Reshetikhin–Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invari...
متن کاملSkein Theory and Witten-reshetikhin-turaev Invariants of Links in Lens Spaces
We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of an arbitrary link in L(p, q) as a function of the level r− 2. They are given by
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 2004