On eigenvalues of double branched covers
Geometric Topology
2019-10-07 v1
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.
Keywords
Cite
@article{arxiv.1709.05617,
title = {On eigenvalues of double branched covers},
author = {Kouki Sato},
journal= {arXiv preprint arXiv:1709.05617},
year = {2019}
}
Comments
13 pages, 15 figures