Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The first-order genus of a knot

PETER D. HORNa1

a1 Mathematics Department, Rice University, 6100 S. Main St., Houston, TX 77005-1892, U.S.A. e-mail: phorn@rice.edu

Abstract

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.

(Received January 16 2008)

(Revised May 16 2008)

Footnotes

† Partially supported by National Science Foundation grant DMS-0240058.