منابع مشابه
n-QUASI-ISOTOPY: I. QUESTIONS OF NILPOTENCE
It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link up to link homotopy can be cancelled in a (componentwise) connected sum with another link. In this paper we address the question whether some form of the ‘complexity accumulation’ property of knots holds for (piecewiselinear) links up to some stronger analogue of link homotopy, which still do...
متن کاملn - QUASI - ISOTOPY : II . COMPARISON
SERGEY A. MELIKHOV and DUŠAN REPOVŠ ABSTRACT We prove that k-quasi-isotopy implies (k + 1)-cobordism of Cochran–Orr, leading to k-quasi-isotopy invariance of Cochran's derived invariants β i , i ≤ k, and Milnor's ¯ µ-invariants of length ≤ 2k + 3. Secondly, k-quasi-isotopic links cannot be distinguished by any Vassiliev invariant of type ≤ k which is well-defined up to PL isotopy, where type ≤ ...
متن کامل5 n - QUASI - ISOTOPY : II . COMPARISON
Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling and relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (resp. contractible open 3-manifold) M if and only if M is homeomorphic to S 3 (resp. R 3). A...
متن کاملn-QUASI-ISOTOPY: III. ENGEL CONDITIONS
In part I it was shown that for each k ≥ 1 the generalized Sato–Levine invariant detects a gap between k-quasi-isotopy of link and peripheral structure preserving isomorphism of the finest quotient Gk of its fundamental group, ‘functorially’ invariant under k-quasi-isotopy. Here we show that Cochran’s derived invariant β, provided k ≥ 3, and a series of μ̄-invariants, starting with μ̄(111112122) ...
متن کاملA Geometric Filtration of Links modulo Knots: I. Questions of Nilpotence
For each k = 0, 1, 2, . . . we define an equivalence relation called k-quasi-isotopy on the set of classical links in R3 up to isotopy in the sense of Milnor (1957), such that all sufficiently close approximations of a topological link are k-quasi-isotopic. Whereas 0-quasi-isotopy coincides with link homotopy, 1-quasi-isotopy is not implied by concordance, with aid of the generalized (lk 6= 0) ...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2005
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216505003968