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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