Surjectivity of certain word maps on PSL(2,C) and SL(2,C)
arXiv:1407.3447
Abstract
We show that an element w of a free group F on n generators defines a surjective word map of PSL(2,C)^n onto PSL(2,C) unless w belongs to the second derived subgroup of F. We also describe certain words maps that are surjective on SL(2,C) x SL(2,C). Here C is the field of complex numbers.
This is a 30-page paper with two authors. We use the Magnus embedding theorem in order to extend the previous results about the surjectiveness of certain word maps from PSL(2)^n to PSL(2) to the case of arbitrary positive integer n