The Blanchfield form and the braid groups
Maxime Bourrigan

The closure of a braid defines a link in the 3-sphere, so every link invariant can be thought of as a function on the braid group. In this talk, we consider the case of the Witt class of the Blanchfield form, a link invariant strictly finer than the link signature. Its homomorphism defect turns out to be linked with the Meyer cocycle and a symplectic representation of the braid group, due to Burau.
The main technical ingredient is a generalisation to infinite cyclic coverings of a result of Lannes, which connects the intersection form of a 4-manifold and the linking form of its boundary.