On eigenvalues of double branched covers

Sato, Kouki

doi:10.1090/proc/14378

On eigenvalues of double branched covers
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Proc. Amer. Math. Soc. 147 (2019), 2707-2722 Request permission

Abstract:

For a given knot, we study the minimal number of positive eigenvalues of the double branched cover over spanning surfaces for the knot. The value gives a lower bound for various genera, the dealternating number and the alternation number of knots, and we prove that Batson’s bound for the non-orientable 4-genus gives an estimate of the value. In addition, we use the value to give a necessary condition for being quasi-alternating.

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