JournalscmhVol. 85, No. 4pp. 751–773

The non-triviality of the Grope filtrations of the knot and link concordance groups

  • Peter D. Horn

    Columbia University, New York, USA
The non-triviality of the Grope filtrations of the knot and link concordance groups cover
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Abstract

We consider the Grope filtration of the classical knot concordance group that was introduced by Cochran, Orr and Teichner. Our main result is that each successive quotient in this filtration has 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.

Cite this article

Peter D. Horn, The non-triviality of the Grope filtrations of the knot and link concordance groups. Comment. Math. Helv. 85 (2010), no. 4, pp. 751–773

DOI 10.4171/CMH/210