Strictly ascending HNN extensions of finite rank free groups that are linear over Z

Abstract

We find strictly ascending HNN extensions of finite rank free groups possessing a presentation 2-complex which is a non positively curved square complex. On showing these groups are word hyperbolic, we have by results of Wise and Agol that they are linear over the integers. An example is the endomorphism of the free group on a,b with inverses A,B that sends a to aBaab and b to bAbba.