Invariants of plane algebraic curves via representations of the braid groups
If two plane curves of the same degree have one to one corresponding singularities which are topologically equivalent, they are said to be equisingular. An equisingular family need not be connected. It is interesting to find invariants which may distinguish the connected components of a family. In a previous paper by the author [Duke Math. J. 49, 833-851 (1982; Zbl 0524.14026)], the Alexander polynomial was shown to have this property. In the note under review the author introduces another invariant to do the job. This invariant, which is defined for any representation of the braid group, is a Laurant polynomial determined up to a unit in the ring \({\mathbb{Q}}[t,t^{-1}]\). In the case of the reduced Burau representation, this invariant essentially coincides with the Alexander polynomial.
scientific article; zbMATH DE number 4103232
scientific article