Concordance Crosscap Numbers of Knots and the Alexander Polynomial
Geometric Topology
2013-10-29 v2
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.
Cite
@article{arxiv.math/0703109,
title = {Concordance Crosscap Numbers of Knots and the Alexander Polynomial},
author = {Charles Livingston},
journal= {arXiv preprint arXiv:math/0703109},
year = {2013}
}
Comments
3 pages, typographical corrections