分野別セミナー

This talk is about invariants of null-homologous knots in rational homology 3-spheres. I will first show that the rational Blanchfield form characterizes these knots up to null Lagrangian-Preserving surgeries. This implies in particular that the rational Blanchfield form is a universal degree 0 invariant of null-homologous knots in Q-spheres with respect to null LP-surgeries. In higher degrees, there are two conjecturally universal finite type invariants, namely the rational lift of the Kontsevich integral constructed by Garoufalidis and Kricker, and the Lescop invariant constructed by means of equivariant intersections in configuration spaces. I will discuss this conjecture in the second part of the talk.