Geodesic
A simple proof of the Crowell–Murasugi theorem
Kindred, Thomas1
1 Department of Mathematics, Wake Forest University, Winston-Salem, NC, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2779-2785

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We give an elementary, self-contained proof of the theorem, proven independently in 1958–1959 by Crowell and Murasugi, that the genus of any oriented nonsplit alternating link equals half the breadth of its Alexander polynomial (with a correction term for the number of link components), and that applying Seifert’s algorithm to any oriented connected alternating link diagram gives a surface of minimal genus.

DOI : 10.2140/agt.2024.24.2779
Keywords: Seifert surface, Alexander polynomial, alternating link, alternating knot, Murasugi sum, plumbing, fiber surface, de-plumbing, knot genus, link genus, 3–genus, Seifert's algorithm, homogeneous link

Kindred, Thomas 1

1 Department of Mathematics, Wake Forest University, Winston-Salem, NC, United States 
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Kindred, Thomas. A simple proof of the Crowell–Murasugi theorem. Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2779-2785. doi: 10.2140/agt.2024.24.2779

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