Rational Blanchfield forms, S-equivalence, and null LP-surgeries - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin de la société mathématique de France Année : 2015

Rational Blanchfield forms, S-equivalence, and null LP-surgeries

Delphine Moussard
  • Fonction : Auteur
  • PersonId : 899828

Résumé

Null Lagrangian-preserving surgeries are a generalization of the Garoufalidis and Rozansky null-moves, that these authors introduced to study the Kricker lift of the Kontsevich integral, in the setting of pairs (M,K) composed of a rational homology sphere M and a null-homologous knot K in M. They are defined as replacements of null-homologous rational homology handlebodies of M\K by other such handlebodies with identical Lagrangian. A null Lagrangian-preserving surgery induces a canonical isomorphism between the rational Alexander modules of the involved pairs, which preserves the Blanchfield form. Conversely, we prove that a fixed isomorphism between rational Alexander modules which preserves the Blanchfield form can be realized, up to multiplication by a power of t, by a finite sequence of null Lagrangian-preserving surgeries. We also prove that such classes of isomorphisms can be realized by rational S-equivalences. In the case of integral homology spheres, we prove similar realization results for a fixed isomorphism between integral Alexander modules.
Fichier principal
Vignette du fichier
Blanchfield_forms_and_LP_surgeries.pdf (269.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00715583 , version 1 (08-07-2012)
hal-00715583 , version 2 (26-03-2013)

Identifiants

Citer

Delphine Moussard. Rational Blanchfield forms, S-equivalence, and null LP-surgeries. Bulletin de la société mathématique de France, 2015, 143 (2), pp.403-431. ⟨hal-00715583v2⟩

Collections

CNRS FOURIER
99 Consultations
120 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More