Finite-type invariants of knots, links, and graphs
نویسندگان
چکیده
منابع مشابه
Finite Type Invariants for Knots
We use the Jaco-Shalen and Johannson theory of the characteristic submanifold and the Torus theorem (Gabai, Casson-Jungreis) to develop an intrinsic finite tvne theory for knots in irreducible 3-manifolds. We also establish _ __ a relation between finite type knot invariants in 3-manifolds and these in R3. existence of non-trivial finite type invariants for knots in irreducible 3-manifolds. rig...
متن کاملClaspers and finite type invariants of links
We introduce the concept of “claspers,” which are surfaces in 3–manifolds with some additional structure on which surgery operations can be performed. Using claspers we define for each positive integer k an equivalence relation on links called “Ck–equivalence,” which is generated by surgery operations of a certain kind called “Ck–moves”. We prove that two knots in the 3–sphere are Ck+1–equivale...
متن کاملQUATERNIONIC INVARIANTS of VIRTUAL KNOTS and LINKS
In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 2×2 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from any classical knot, including the unknot. The contents of the paper are as follows
متن کاملInvariants of Random Knots and Links
We study random knots and links in R using the Petaluma model, which is based on the petal projections developed in [2]. In this model we obtain a formula for the distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the higher moments of the Casson invariant and the order-3 knot invariant v3. These are the first precise formulas giv...
متن کاملFinite Type Invariants and Milnor Invariants for Brunnian Links
A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any Goussarov-Vassiliev finite type invariant of (n + 1)component links of degree < 2n is trivial. The purpose of this paper is to study the first nontrivial case. We show that the restriction of an invariant of degree 2n to ...
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ژورنال
عنوان ژورنال: Topology
سال: 1996
ISSN: 0040-9383
DOI: 10.1016/0040-9383(95)00056-9