$ {L}^{2}$-Alexander invariant for torus knots

Jérôme Dubois; Christian Wegner

doi:10.1016/j.crma.2010.10.008

Geometry/Topology

L^{2}

-Alexander invariant for torus knots

Presented by: Étienne Ghys

Jérôme Dubois ¹; Christian Wegner ²

¹Institut de mathématiques de Jussieu, Université Paris Diderot–Paris 7, UFR de mathématiques, case 7012, bâtiment Chevaleret, 2, place Jussieu, 75205 Paris cedex 13, France
²Mathematisches Institut der WWU Münster, Einsteinstraße 62, 48149 Münster, Germany

Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1185-1189

Abstract (Original language)
Résumé

The aim of this Note is to present the explicit computation of the $L^{2}$ -Alexander invariant (defined by Li and Zhang, 2006 [5,6]) for all torus knots.

Le but de cette Note est de calculer explicitement l'invariant d'Alexander $L^{2}$ (défini par Li et Zhang, 2006 [5,6]) dans le cas des nœuds toriques.

Received: 2010-04-07
Accepted: 2010-10-11
Published online: 2010-11-01

DOI: 10.1016/j.crma.2010.10.008

Author's affiliations:

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

@article{CRMATH_2010__348_21-22_1185_0,
     author = {J\'er\^ome Dubois and Christian Wegner},
     title = {$ {L}^{2}${-Alexander} invariant for torus knots},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1185--1189},
     year = {2010},
     publisher = {Elsevier},
     volume = {348},
     number = {21-22},
     doi = {10.1016/j.crma.2010.10.008},
     language = {en},
}

TY  - JOUR
AU  - Jérôme Dubois
AU  - Christian Wegner
TI  - $ {L}^{2}$-Alexander invariant for torus knots
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1185
EP  - 1189
VL  - 348
IS  - 21-22
PB  - Elsevier
DO  - 10.1016/j.crma.2010.10.008
LA  - en
ID  - CRMATH_2010__348_21-22_1185_0
ER  -

%0 Journal Article
%A Jérôme Dubois
%A Christian Wegner
%T $ {L}^{2}$-Alexander invariant for torus knots
%J Comptes Rendus. Mathématique
%D 2010
%P 1185-1189
%V 348
%N 21-22
%I Elsevier
%R 10.1016/j.crma.2010.10.008
%G en
%F CRMATH_2010__348_21-22_1185_0

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

References
Cited by

[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, $L^{2}$ -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 $L^{2}$ -Alexander invariant for knots, Commun. Contemp. Math., Volume 8 (2006) no. 2, pp. 167-187

[6] W. Li; W. Zhang An $L^{2}$ -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 $L^{2}$ -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 $L^{2}$ -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

Cited by Sources:

Comments - Policy