The First-Order Genus of a Knot

Details The First-Order Genus of a Knot The First-Order Genus of a Knot

2007-12-06

arxiv.org/abs/0712.1010v1

Mathematics

Geometric Topology

14 pages, 17 figures

Scientific paper

10.1017/S0305004108001886

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.

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