The First-Order Genus of a Knot
arXiv:0712.1010 · doi:10.1017/S0305004108001886
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.
14 pages, 17 figures