On the Alexander invariants of trigonal curves

On the Alexander invariants of hypersurface complements

On Reciprocality of Twisted Alexander Invariants

Given a knot and an SLnC representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL3Z representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal.

The Alexander Module of a Trigonal Curve. Ii

We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

Alexander Invariants and Transversality

We show that some of the main results in Laurentiu Maxim’s paper [10] can be obtained (even in a slightly more general setting) using the theory of perverse sheaves of finite rank over Q as described for instance in author’s recent book [3].

Dihedral Coverings of Trigonal Curves

We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve D with a singular point of multiplicity (deg D−3).