### Abstract

We introduce a geometric invariant of knots in S^{3}, 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.

Original language | English (US) |
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Pages (from-to) | 135-149 |

Number of pages | 15 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 146 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2009 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Horn, P. D. (2009). The first-order genus of a knot.

*Mathematical Proceedings of the Cambridge Philosophical Society*,*146*(1), 135-149. https://doi.org/10.1017/S0305004108001886