Cosmetic crossings and Seifert matrices

Balm, Cheryl; Friedl, Stefan; Kalfagianni, Efstratia et Powell, Mark (2012). « Cosmetic crossings and Seifert matrices ». Communications in Analysis and Geometry, 20(2), pp. 235-253.

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Résumé

We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for twisted Whitehead doubles of non-cable knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 12 crossings.

Type: Article de revue scientifique
Mots-clés ou Sujets: Seifert matrices, knots
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Mark Powell
Date de dépôt: 27 avr. 2016 13:36
Dernière modification: 19 mai 2016 18:13
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8335

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