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Knot concordance and
higher-order Blanchfield duality
Tim D Cochran, Shelly Harvey and Constance Leidy |
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Geometry & Topology 13 (2009) 1419–1482
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Abstract |
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In 1997, T Cochran, K Orr, and P Teichner [Ann. of Math. (2) 157 (2003) 433-519] defined a filtration of the classical knot concordance group , The filtration is important because of its strong connection to the classification of topological –manifolds. Here we introduce new techniques for studying and use them to prove that, for each , the group has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson–Gordon and Gilmer, contain slice knots. |
Keywords
concordance, (n)-solvable, knot, slice knot, Blanchfield
form, von Neumann signature
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M10
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References |
Publication
Received: 10 September 2008
Accepted: 1 December 2008
Published: 19 February 2009
Proposed: Peter Teichner
Seconded: Cameron Gordon, Tom Goodwillie
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Authors |
| Tim D Cochran | |
| Department of Mathematics Rice University Houston, Texas 77005-1892 |
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| http://math.rice.edu/~cochran | |
| Shelly Harvey | |
| Department of Mathematics Rice University Houston, Texas 77005-1892 |
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| http://math.rice.edu/~shelly | |
| Constance Leidy | |
| Wesleyan University Wesleyan Station Middletown, CT 06459 |
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| http://cleidy.web.wesleyan.edu | |
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