ON VASSILIEV INVARIANTS FOR ALGEBRAICALLY SPLIT LINKS
نویسندگان
چکیده
منابع مشابه
On Jones knot Invariants and Vassiliev Invariants
We show that the n-th derivative of a quantum group invariant, evaluated at 1, is a Vassiliev invariant while the derivative of the Jones polynomial, evaluated at a real number 6 = 1, is not a Vassiliev in variant. The coeecients of the classical Conway polynomial are known to be Vassiliev invariants. We show that the coeecients of the Jones polynomial are not vassiliev invariants.
متن کاملUniversal Vassiliev invariants of links in coverings of 3-manifolds
We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M . We construct universal Vassiliev invariants of links in M , where M = P 2×[0, 1] is a cylinder over the real projective plane P 2, M = Σ× [0, 1] is a cylinder over a surface Σ with boundary, and M = S1 × S2. A finite covering p : N −→ M induces a map π1(p) ∗ betwe...
متن کاملIntegrality of the Averaged Jones Polynomial of Algebraically Split Links
n!φn(L) ∈ 6Z. This conjecture is verified for n = 1, 2 in [LW], and we consider the case n ≥ 3 here. We first establish that an(L) ∈ Z whenever L is a geometrically split link (GSL), implying that φn(L) ∈ 2Z, which is a priori stronger than the conjecture in this case. Nevertheless, Conjecture 4.1 is not true for ASLs. The problem is the presence of additional factors of 2 in the denominator of...
متن کاملOn the Vassiliev Knot Invariants
The theory of knot invariants of finite type (Vassiliev invariants) is described. These invariants turn out to be at least as powerful as the Jones polynomial and its numerous generalizations coming from various quantum groups, and it is conjectured that these invariants are precisely as powerful as those polynomials. As invariants of finite type are much easier to define and manipulate than th...
متن کاملVassiliev invariants for braids on surfaces
We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface. 1 Definitions and statements 1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 1998
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216598000413