English

Knots with many minimal genus Seifert surfaces

Geometric Topology 2013-10-30 v3

Abstract

Roberts proved that a family of alternating, arborescent, prime knots each have at least 22n12^{2n-1} distinct minimal genus Seifert surfaces, where nn is the genus of the knot in question. We give a subfamily of these knots that have exactly this many minimal genus Seifert surfaces.

Keywords

Cite

@article{arxiv.1308.3218,
  title  = {Knots with many minimal genus Seifert surfaces},
  author = {Jessica E. Banks},
  journal= {arXiv preprint arXiv:1308.3218},
  year   = {2013}
}

Comments

3 pages, 2 figures. Version 2: corrections arising from a difference in definitions, reference added

R2 v1 2026-06-22T01:09:27.823Z