A Formula in the Theory of Finite Type Invariants
نویسنده
چکیده
A family Ck+1 of local moves on knot diagrams for each positive integer k, is defined in [1] where it is also shown that two knots are Ck+1equivalent iff all of their Vassiliev-Gusarov invariants of degree k agree. Every move Ck+1 splits the space K of knots into equivalence classes and defines a metric on each equivalence class. For two Ck+1-equivalent knots K, J with dCk+1 (K, J) = 1 we give a formula for the difference vk+1(K)−vk+1(J). From this we deduce a formula for the difference of the degree k + 1 invariants of two knots all of whose degree k Vassiliev invariants coincide.
منابع مشابه
ON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملFermat limit and congruence of Ohtsuki invariants
By calculating the Fermat limit of certain q–Fermat functions, we get explicit surgery formulae for the second and third Ohtsuki invariants for homology 3–spheres. The surgery formula of the second Ohtsuki invariant λ2 , combined with an argument using the general theory of finite type invariants of homology 3–spheres, leads to a congruence relation between the first and second Ohtsuki invarian...
متن کاملCharacteristics of Categories And
In a previous article, we introduced notions of finiteness obstruction , Euler characteristic, and L 2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homo-topy colimits of I-indexed categories where I is any small category admitting a finite I-CW-model for its I-classifying space. Special cases of our Homotopy Colimit Formul...
متن کاملSingular link Floer homology
We define a grid presentation for singular links, i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler characteristic vanish. Introduction Since the Jones polynomial was categorifi...
متن کاملNew Improvement in Interpretation of Gravity Gradient Tensor Data Using Eigenvalues and Invariants: An Application to Blatchford Lake, Northern Canada
Recently, interpretation of causative sources using components of the gravity gradient tensor (GGT) has had a rapid progress. Assuming N as the structural index, components of the gravity vector and gravity gradient tensor have a homogeneity degree of -N and - (N+1), respectively. In this paper, it is shown that the eigenvalues, the first and the second rotational invariants of the GGT (I1 and ...
متن کامل