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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Polynomial splittings of metabelian von Neumann rho–invariants of knots
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by Se-Goo Kim and Taehee Kim PDF
Proc. Amer. Math. Soc. 136 (2008), 4079-4087 Request permission

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
  • MR Author ID: 610250
  • ORCID: 0000-0002-8874-9408
  • Email: sgkim@khu.ac.kr
  • Taehee Kim
  • Affiliation: Department of Mathematics, Konkuk University, Seoul 143–701, Korea
  • MR Author ID: 743933
  • Email: tkim@konkuk.ac.kr
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 4079-4087
  • MSC (2000): Primary 57M25; Secondary 57N70
  • DOI: https://doi.org/10.1090/S0002-9939-08-09372-6
  • MathSciNet review: 2425750