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.References
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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