The Non-triviality of the Grope Filtrations of The Knot and Link Concordance Groups

Details The Non-triviality of the Grope Filtrations of The Knot and Link Concordance Groups The Non-triviality of the Grope Filtrations of The Knot and Link Concordance Groups

2008-04-16

arxiv.org/abs/0804.2661v1

Mathematics

Geometric Topology

16 pages, 14 figures

Scientific paper

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.

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