Homology gives rise to representations of braid groups (Lawrence, 1990).
Bigelow showed that some well-known link invariants can be constructed from
these (Jones and Homfly polynomials). I will construct a seemingly new
link invariant from them. It depends on a variable t and a root of unity q.
It would be interesting if it could be defined for a variable q
(it doesn't seem to be a polynomial in q).