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The concordance classification of low crossing number knots


Authors: Julia Collins, Paul Kirk and Charles Livingston
Journal: Proc. Amer. Math. Soc. 143 (2015), 4525-4536
MSC (2010): Primary 57M25; Secondary 57N70, 57Q45
DOI: https://doi.org/10.1090/proc/12587
Published electronically: April 29, 2015
MathSciNet review: 3373950
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Abstract: We present the complete classification of the subgroup of the classical knot concordance group generated by prime knots with eight or fewer crossings. Proofs are presented in summary. We also describe extensions of this work to the case of nine crossing knots.


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Additional Information

Julia Collins
Affiliation: School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Scotland, EH9 3JZ
Email: Julia.Collins@ed.ac.uk

Paul Kirk
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: pkirk@indiana.edu

Charles Livingston
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: livingst@indiana.edu

DOI: https://doi.org/10.1090/proc/12587
Received by editor(s): November 19, 2013
Received by editor(s) in revised form: June 15, 2014
Published electronically: April 29, 2015
Additional Notes: This work was supported in part by the National Science Foundation under Grant 1007196, and by Simons Foundation Grants 278714 and 209082.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2015 American Mathematical Society