Communications in Analysis and Geometry

We use Klyachko's methods to prove that, if a 1-cell and a 2-cell are added to a complex with torsion free fundamental group, and with the 2-cell attached by an amenable t-shape, then the second homotopy group changes by extension of scalars. It then follows using a result of Bogley and Pride that the resulting fundamental group is also torsion free. We also prove that the normal closure of the attaching word contains no words of smaller complexity.

- postscript file
- published article (in postscript, pdf)