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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Concordance crosscap numbers of knots and the Alexander polynomial
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by Charles Livingston PDF
Proc. Amer. Math. Soc. 136 (2008), 3351-3353 Request permission

Abstract:

For a knot $K$ the concordance crosscap number, $c(K)$, is the minimum crosscap number among all knots concordant to $K$. Building on work of G. Zhang, which studied the determinants of knots with $c(K) < 2$, we apply the Alexander polynomial to construct new algebraic obstructions to $c(K) < 2$. With the exception of low crossing number knots previously known to have $c(K) < 2$, the obstruction applies to all but four prime knots of 11 or fewer crossings.
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Additional Information
  • Charles Livingston
  • Affiliation: Department of Mathematics, Indiana University, 123 Rawles Hall, Bloomington, Indiana 47405
  • MR Author ID: 193092
  • Received by editor(s): May 11, 2007
  • Published electronically: April 25, 2008
  • Communicated by: Daniel Ruberman
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3351-3353
  • MSC (2000): Primary 57M25
  • DOI: https://doi.org/10.1090/S0002-9939-08-09481-1
  • MathSciNet review: 2407102