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Filtrations of the knot concordance group
by
Shelly Harvey
Rice University
Coauthors: Tim Cochran (Rice University)
Constance Leidy (Wesleyan University)
In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration Fn of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. For each n, we give an explicit family of knots that generates a Z∞ subgroup of Fn/Fn.5. Moreover, for each n, we show that there are an infinite number of different Z∞ subgroups of Fn/Fn.5. We establish the same result for the corresponding filtration of the smooth concordance group.
Paper reference: arXiv:0710.3082
Date received: May 14, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxb-17.