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 language||English (US)|
|Number of pages||15|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - Jan 2009|
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