ALEXANDER GROUPS AND VIRTUAL LINKS

Abstract

The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants Δ i (u 1 ,…,u d , v), i=0, 1,…, is obtained. When l is a classical link, Δ i reduces to the well-known ith Alexander polynomial of the link in the d variables u 1 v,…,u d v; in particular, Δ 0 vanishes.