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

Delphine Moussard
2015 Bulletin de la Société Mathématique de France  
Garoufalidis and Rozansky introduced null-moves on the set of pairs (M, K), where M is an integral homology sphere and K is a knot in M . These null-moves are suitable to study the Kricker lift of the Kontsevich integral. They defined a filtration on the space generated by pairs (M, K) up to orientation-preserving homeomorphism. This filtration splits with respect to the isomorphism classes of integral Alexander modules equipped with their Blanchfield forms. Null Lagrangianpreserving surgeries
more » ... eserving surgeries are a generalization of the Garoufalidis and Rozansky null-moves in the setting of pairs (M, K) composed of a rational homology sphere M and a nullhomologous 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. We prove that two pairs (M, K) can be obtained from one another by a finite sequence of null Lagrangian-preserving surgeries if and only if they have isomorphic rational Alexander modules and Blanchfield forms. MSC: 57M25 57M27 57N10 57N65 Keywords: Alexander module; Blanchfield form; equivariant linking pairing; homology sphere; homology handlebody; Lagrangian-preserving surgery; Seifert matrix; S-equivalence; lift of the Kontsevich integral; null-move; Euler degree of the Kontsevich integral.
doi:10.24033/bsmf.2693 fatcat:vl2nxt4penghbmjeybalzxb23q