The Blanchfield form and the braid groups
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.