Ascending HNN extensions of finitely generated free groups are Hopfian
by
Michael Mihalik
Vanderbilt University
Coauthors: Ross Geoghegan (SUNY Binghamton), Mark Sapir (Vanderbilt University), Daniel Wise (Cornell University)

We discuss the following cohomological dimension raising result for ascending HNN extensions.

Theorem 1. Let n >= 0. Suppose H is a torsion-free group of type FP_n such that H^k(H;ZH)=0 for

2 <= k <= n-1 and cd(H)=n. If \tau:H --> H is a monomorphism and G = H * _\tau, then cd(G)=n+1.

The case n=2, of Theorem 1, is a key ingredient in the proof of:

Theorem 2. Every ascending HNN extension of a finitely generated free group is Hopfian.

Date received: May 21, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cada-12.