The aim of this note is to prove that the -Alexander invariant, a knot invariant defined using -torsions, detects the unknot.
Le but de cette note est de démontrer que lʼinvariant dʼAlexander , un invariant de nœuds défini via des torsions , détecte le nœud trivial.
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Fathi Ben Aribi 1
@article{CRMATH_2013__351_5-6_215_0, author = {Fathi Ben Aribi}, title = {The $ {L}^{2}${-Alexander} invariant detects the unknot}, journal = {Comptes Rendus. Math\'ematique}, pages = {215--219}, publisher = {Elsevier}, volume = {351}, number = {5-6}, year = {2013}, doi = {10.1016/j.crma.2013.03.009}, language = {en}, }
Fathi Ben Aribi. The $ {L}^{2}$-Alexander invariant detects the unknot. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 215-219. doi : 10.1016/j.crma.2013.03.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.03.009/
[1] 3-Manifold groups, 2012 | arXiv
[2] Elliptic operators, discrete groups and von Neumann algebras, Orsay, 1974 (Astérisque), Volume vols. 32–33, Soc. Math. France, Paris (1976), pp. 43-72
[3] Knots, de Gruyter Stud. Math., vol. 5, Walter de Gruyter, 2003
[4] J. Dubois, S. Friedl, The -Alexander torsion, in preparation.
[5] J. Dubois, C. Wegner, -Alexander invariant for knots, in preparation.
[6] An -Alexander invariant for knots, Commun. Contemp. Math., Volume 8 (2006) no. 2, pp. 167-187
[7] -Invariants: Theory and Applications to Geometry and K-Theory, Ergeb. Math. Grenzgeb. (3), vol. 44, Springer-Verlag, Berlin, 2002
[8] A duality theorem for Reidemeister torsion, Ann. Math., Volume 76 (1962), pp. 134-147
[9] The colored Jones polynomials and the simplicial volume of a knot, Acta Math., Volume 186 (2001), pp. 85-104
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