The first-order genus of a knot

Peter D. Horn

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce a geometric invariant of knots in S3, 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 languageEnglish (US)
Pages (from-to)135-149
Number of pages15
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
StatePublished - Jan 2009

ASJC Scopus subject areas

  • General Mathematics


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