On the cube of the equivariant linking pairing for knots and 3-manifolds of rank one
From MaRDI portal
Publication:6220436
arXiv1008.5026MaRDI QIDQ6220436
Publication date: 30 August 2010
Abstract: Let M be a closed oriented 3-manifold with first Betti number one. Its equivariant linking pairing may be seen as a two-dimensional cohomology class in an appropriate infinite cyclic covering of the space of ordered pairs of distinct points of M. We show how to define the equivariant cube Q(K) of this Blanchfield pairing with respect to a framed knot K that generates H_1(M)/Torsion. This article is devoted to the study of the invariant Q. We prove many properties for this invariant including two surgery formulae. Via surgery, the invariant Q is equivalent to an invariant of null-homologous knots in rational homology spheres, that coincides with the two-loop part of the Kricker rational lift of the Kontsevich integral, at least for knots with trivial Alexander polynomial in integral homology spheres.
This page was built for publication: On the cube of the equivariant linking pairing for knots and 3-manifolds of rank one
