Finite Type Invariants
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چکیده
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics.
منابع مشابه
Finite Type Invariants of 3-Manifolds
Contents 1 Introduction 2 2 Finiteness 13 3 The Conway polynomial 20 4 Finite type invariants from quantum invariants 30 5 Combinatorial structure of finite type invariants 47 6 Finite type invariants for spin manifolds 58 7 Finite type invariants for bounded manifolds 61 8 Finite type invariants for marked manifolds 62 9 Further generalizations 65 10 Relationships with other theories and other...
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 کاملFinite Type Link Invariants and the Non-invertibility of Links
We show that a variation of Milnor’s μ̄-invariants, the so-called Campbell-Hausdorff invariants introduced recently by Stefan Papadima, are of finite type. This implies, in particular, that finite type link invariants can detect the non-invertibility of a link with more than one components and they are thus stronger than quantum invariants. It is still open whether finite type knot invariants (V...
متن کاملOn Finite Type 3-manifold Invariants Iii: Manifold Weight Systems
The present paper is a continuation of [Oh2] and [GL] devoted to the study of finite type invariants of integral homology 3-spheres. We introduce the notion of manifold weight systems, and show that type m invariants of integral homology 3-spheres are determined (modulo invariants of type m − 1) by their associated manifold weight systems. In particular we deduce a vanishing theorem for finite ...
متن کاملCharacterization 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...
متن کاملFinite Type Invariants of Integral Homology 3-spheres: a Survey
We are now embarrassingly rich in knot and 3-manifold invariants. We have to organize these invariants systematically and find out ways to make use of them. The theory of finite type knot invariants, or Vassiliev invariants, has been very successful in accomplishing the first task. Recently, an analogous theory of finite type invariants of integral homology 3-spheres started to emerge. The anal...
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