Periodic spanning surfaces of periodic knots
Geometric Topology
2021-01-13 v1
Abstract
Edmonds famously proved that every periodic knot of genus g possesses an equivariant Seifert surface of genus g. We show that this is not true if one instead considers nonorientable spanning surfaces of a periodic knot. We demonstrate by example that the difference between the first Betti number of an equivariant and a nonequivariant nonorientable spanning surface of a periodic knot, can be arbitrarily large.
Keywords
Cite
@article{arxiv.2101.04668,
title = {Periodic spanning surfaces of periodic knots},
author = {Stanislav Jabuka},
journal= {arXiv preprint arXiv:2101.04668},
year = {2021}
}
Comments
3 pages, 1 figure