Comptes Rendus
Geometry/Topology
L2-Alexander invariant for torus knots
[Invariant d'Alexander L2 pour les nœuds toriques]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1185-1189.

Le but de cette Note est de calculer explicitement l'invariant d'Alexander L2 (défini par Li et Zhang, 2006 [5,6]) dans le cas des nœuds toriques.

The aim of this Note is to present the explicit computation of the L2-Alexander invariant (defined by Li and Zhang, 2006 [5,6]) for all torus knots.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.008

Jérôme Dubois 1 ; Christian Wegner 2

1 Institut de mathématiques de Jussieu, Université Paris Diderot–Paris 7, UFR de mathématiques, case 7012, bâtiment Chevaleret, 2, place Jussieu, 75205 Paris cedex 13, France
2 Mathematisches Institut der WWU Münster, Einsteinstraße 62, 48149 Münster, Germany
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     author = {J\'er\^ome Dubois and Christian Wegner},
     title = {$ {L}^{2}${-Alexander} invariant for torus knots},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1185--1189},
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     doi = {10.1016/j.crma.2010.10.008},
     language = {en},
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Jérôme Dubois; Christian Wegner. $ {L}^{2}$-Alexander invariant for torus knots. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1185-1189. doi : 10.1016/j.crma.2010.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.008/

[1] G. Burde; H. Zieschang Knots, de Gruyter Studies in Mathematics, vol. 5, Walter de Gruyter, 2003

[2] J. Cheeger Analytic torsion and the heat equation, Ann. Math., Volume 109 (1979), pp. 259-322

[3] J. Dubois, C. Wegner, L2-Alexander invariant for knots, in preparation.

[4] S. Friedl; S. Vidussi A survey of twisted Alexander polynomials, 2009 (preprint) | arXiv

[5] W. Li; W. Zhang An L2-Alexander invariant for knots, Commun. Contemp. Math., Volume 8 (2006) no. 2, pp. 167-187

[6] W. Li; W. Zhang An L2-Alexander–Conway invariant for knots and the volume conjecture, Differential Geometry and Physics, Nankai Tracts Math., vol. 10, World Sci. Publ., Hackensack, NJ, 2006, pp. 303-312

[7] W. Lück L2-Invariants: Theory and Applications to Geometry and K-Theory, Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 44, Springer-Verlag, Berlin, 2002

[8] W. Lück; T. Schick L2-torsion of hyperbolic manifolds of finite volume, Geometric and Functional Analysis, Volume 9 (1999), pp. 518-567

[9] J. Milnor A duality theorem for Reidemeister torsion, Ann. of Math., Volume 76 (1962), pp. 134-147

[10] W. Müller Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math., Volume 28 (1978), pp. 233-305

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