A simple proof of the Crowell–Murasugi theorem
Year: 2024
Type: article
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.
Source: Algebraic & Geometric Topology
Author: Thomas Kindred
Institution: Wake Forest University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4401865007