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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomial splittings of metabelian von Neumann rho-invariants of knots


Authors: Se-Goo Kim and Taehee Kim
Journal: Proc. Amer. Math. Soc. 136 (2008), 4079-4087
MSC (2000): Primary 57M25; Secondary 57N70
Published electronically: June 4, 2008
MathSciNet review: 2425750
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Abstract: We show that if the connected sum of two knots with coprime Alexander polynomials has vanishing von Neumann $ \rho$-invariants associated with certain metabelian representations, then so do both knots. As an application, we give a new example of an infinite family of knots which are linearly independent in the knot concordance group.


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Additional Information

Se-Goo Kim
Affiliation: Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130–701, Korea
Email: sgkim@khu.ac.kr

Taehee Kim
Affiliation: Department of Mathematics, Konkuk University, Seoul 143–701, Korea
Email: tkim@konkuk.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09372-6
PII: S 0002-9939(08)09372-6
Keywords: Knot, concordance, polynomial splitting
Received by editor(s): May 11, 2007
Received by editor(s) in revised form: October 8, 2007
Published electronically: June 4, 2008
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 American Mathematical Society