The Non-triviality of the Grope Filtrations of the Knot and Link Concordance Groups
نویسنده
چکیده
We consider the Grope filtration of the classical knot concordance group that was introduced in a paper of Cochran, Orr and Teichner. Our main result is that successive quotients at each stage in this filtration have infinite rank. We also establish the analogous result for the Grope filtration of the concordance group of string links consisting of more than one component.
منابع مشابه
Non-triviality of the Cochran-orr-teichner Filtration of the Knot Concordance Group
We establish nontriviality results for certain filtrations of the smooth and topological knot concordance groups. First, as regards the n-solvable filtration of the topological knot concordance group, C, defined by K. Orr, P. Teichner and the first author [COT1]: 0 ⊂ · · · ⊂ F(n.5) ⊂ F(n) ⊂ · · · ⊂ F(1.5) ⊂ F(1.0) ⊂ F(0.5) ⊂ F(0) ⊂ C, we refine the recent nontriviality results of Cochran and Te...
متن کاملHigher-order Alexander Invariants and Filtrations of the Knot Concordance Group
We establish certain “nontriviality” results for several filtrations of the smooth and topological knot concordance groups. First, as regards the n-solvable filtration of the topological knot concordance group, C, defined by K. Orr, P. Teichner and the first author: 0 ⊂ · · · ⊂ F(n.5) ⊂ F(n) ⊂ · · · ⊂ F(1.5) ⊂ F(1.0) ⊂ F(0.5) ⊂ F(0) ⊂ C, we refine the recent nontriviality results of Cochran and...
متن کاملWhitney tower concordance of classical links
This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney...
متن کاملGrope Cobordism of Classical Knots
Motivated by the lower central series of a group, we define the notion of a grope cobordism between two knots in a 3-manifold. Just like an iterated group commutator, each grope cobordism has a type that can be described by a rooted unitrivalent tree. By filtering these trees in different ways, we show how the Goussarov-Habiro approach to finite type invariants of knots is closely related to ou...
متن کاملCovering Link Calculus and Iterated Bing Doubles
We give a new geometric obstruction to the iterated Bing double of a knot being a slice link: for n > 1 the (n + 1)st iterated Bing double of a knot is rationally slice if and only if the nth iterated Bing double of the knot is rationally slice. The main technique of the proof is a covering link construction simplifying a given link. We prove certain similar geometric obstructions for n ≤ 1 as ...
متن کامل