The concordance classification of low crossing number knots
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- by Julia Collins, Paul Kirk and Charles Livingston PDF
- Proc. Amer. Math. Soc. 143 (2015), 4525-4536 Request permission
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.References
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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
- MR Author ID: 266369
- Email: pkirk@indiana.edu
- Charles Livingston
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 193092
- Email: livingst@indiana.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4525-4536
- MSC (2010): Primary 57M25; Secondary 57N70, 57Q45
- DOI: https://doi.org/10.1090/proc/12587
- MathSciNet review: 3373950