Concordance Crosscap Numbers of Knots and the Alexander Polynomial

Details Concordance Crosscap Numbers of Knots and the Alexander Polynomial Concordance Crosscap Numbers of Knots and the Alexander Polynomial

2007-03-04

arxiv.org/abs/math/0703109v2

Proc. Amer. Math. Soc. 136 (2008) 3351-3353.

Mathematics

Geometric Topology

3 pages, typographical corrections

Scientific paper

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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