Primary decomposition and the fractal nature of knot concordance
نویسندگان
چکیده
منابع مشابه
Primary Decomposition and the Fractal Nature of Knot Concordance
For each sequence P = (p1(t), p2(t), . . . ) of polynomials we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S, such a sequence of polynomials arises naturally as the orders of certain submodules of a sequence of higher-order Alexander modules of K. These group series yield filtrations of the knot concordance group that refine the (n)-solv...
متن کاملKnot Concordance
We prove the nontriviality at all levels of the filtration of the classical topological knot concordance group C · · · ⊆ Fn ⊆ · · · ⊆ F1 ⊆ F0 ⊆ C. defined in [COT]. This filtration is significant because not only is it strongly connected to Whitney tower constructions of Casson and Freedman, but all previously-known concordance invariants are related to the first few terms in the filtration. In...
متن کاملKnot Concordance and Torsion
The classical knot concordance group, C1, was defined in 1961 by Fox [F]. He proved that it is nontrivial by finding elements of order two; details were presented in [FM]. Since then one of the most vexing questions concerning the concordance group has been whether it contains elements of finite order other than 2–torsion. Interest in this question was heightened by Levine’s proof [L1, L2] that...
متن کاملThe Algebraic Concordance Order of a Knot
Since the inception of knot concordance, questions related to torsion in the concordance group, C1, have been of particular interest; see for instance [6, 8, 14]. The only known torsion in C1 is 2–torsion, arising from amphicheiral knots, whereas Levine’s analysis of higher dimensional concordance revealed far more 2–torsion and also 4–torsion in C2n−1, n > 1. Casson and Gordon [1, 2] demonstra...
متن کاملThe concordance genus of a knot, II
The concordance genus of a knot K is the minimum three-genus among all knots concordant to K . For prime knots of 10 or fewer crossings there have been three knots for which the concordance genus was unknown. Those three cases are now resolved. Two of the cases are settled using invariants of Levine’s algebraic concordance group. The last example depends on the use of twisted Alexander polynomi...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2010
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-010-0604-5