Characterization of finite type string link invariants of degree <5
نویسندگان
چکیده
منابع مشابه
Characterization of Finite Type String Link
In this paper, we give a complete set of finite type string link invariants of degree < 5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closure of (cabled) string links. We show that finite type invariants classify string links up to Ck-moves for k ≤ 5, which proves, at low degree, a conjecture due to Goussar...
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The Vassiliev-Gusarov link invariants of nite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V 1 containing elements g i satisfying the usual braid group relations and elements a i satisfying g i ? g ?1 i = a i , where is a formal variable that may be regarded as me...
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An explicit polynomial in the linking numbers lij and Milnor's triple linking numbers µ(rst) on six component links is shown to be a well-defined finite type link-homotopy invariant. This solves a problem raised by B. Mellor and D. Thurston. An extension of our construction also produces a finite type link invariant which detects the invertibility for some links.
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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...
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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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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2010
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004110000046