منابع مشابه
Vassiliev Homotopy String Link Invariants
We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular, Vassiliev invariants classify string links up to homotopy, and all Vassiliev homotopy string link invariants come from marked surfaces as in [3], using the same construction that in the case of knots gives...
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We study the new formulas of Th. Fiedler for the degree-3-Vassiliev invariants for knots in the 3-sphere and solid torus and present some results obtained by them. We show that a knot with Jones polynomial consisting of exactly two monomials must have at least 20 crossings.
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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack’s second rack cohomology satisfying a new degeneracy conditio...
متن کاملFINITE TYPE LINK HOMOTOPY INVARIANTS II: Milnor’s ¯µ-invariants
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's link homotopy invariant ¯ µ(ijk) is a finite type invariant, of type 1, in this sense. We also generalize this approach to Milnor's higher order ¯ µ invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite t...
متن کاملApproximating Jones Coefficients and Other Link Invariants by Vassiliev Invariants
We find approximations by Vassiliev invariants for the coefficients of the Jones polynomial and all specializations of the HOMFLY and Kauffman polynomials. Consequently, we obtain approximations of some other link invariants arising from the homology of branched covers of links.
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ژورنال
عنوان ژورنال: Topology
سال: 1971
ISSN: 0040-9383
DOI: 10.1016/0040-9383(71)90034-6