A simple proof of the Crowell-Murasugi theorem
Geometric Topology
2024-08-28 v1
Abstract
We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowell and Murasugi, that the genus of an alternating knot equals half the breadth of its Alexander polynomial, and that applying Seifert's algorithm to any alternating knot diagram gives a surface of minimal genus.
Keywords
Cite
@article{arxiv.2209.09850,
title = {A simple proof of the Crowell-Murasugi theorem},
author = {Thomas Kindred},
journal= {arXiv preprint arXiv:2209.09850},
year = {2024}
}
Comments
6 pages, 1 figure, comments welcome!