English

The First-Order Genus of a Knot

Geometric Topology 2009-11-13 v1

Abstract

We introduce a geometric invariant of knots in the three-sphere, called the first-order genus, that is derived from certain 2-complexes called gropes, and we show it is computable for many examples. While computing this invariant, we draw some interesting conclusions about the structure of a general Seifert surface for some knots.

Keywords

Cite

@article{arxiv.0712.1010,
  title  = {The First-Order Genus of a Knot},
  author = {Peter Horn},
  journal= {arXiv preprint arXiv:0712.1010},
  year   = {2009}
}

Comments

14 pages, 17 figures

R2 v1 2026-06-21T09:51:23.408Z