The First-Order Genus of a Knot
Geometric Topology
2009-11-13 v1
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.
Cite
@article{arxiv.0712.1010,
title = {The First-Order Genus of a Knot},
author = {Peter Horn},
journal= {arXiv preprint arXiv:0712.1010},
year = {2009}
}
Comments
14 pages, 17 figures