منابع مشابه
Link invariants from finite racks
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 کاملLink Invariants of Finite Type andPerturbation
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...
متن کامل0 Finite Type Link - Homotopy Invariants
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.
متن کاملOn Finite Racks and Quandles
We revisit finite racks and quandles using a perspective based on permutations which can aid in the understanding of the structure. As a consequence we recover old results and prove new ones. We also present and analyze several examples.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2011
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216511009273