A simple proof of the Crowell-Murasugi theorem
arXiv:2209.09850 · doi:10.2140/agt.2024.24.2779
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.
6 pages, 1 figure, comments welcome!