Stably Free Modules over the Klein Bottle

Introduction
Constructing a Stably Free Module
Applications to the Klein Bottle
Euler Characteristic
We would like to classify all homotopy types of (G, 2)-complexes
with a fixed Euler Characteristic n.
Theorem (Asphericity)
The Klein bottle, with χ(X ) = 0, has the minimal Euler
characteristic of all (G, 2)-complexes. Furthermore, the Klein
Bottle is the only (G, 2)-complex with Euler characteristic equal to
0, up to homotopy.
We use Algebra to next classify (G, 2)-complexes with Euler
characteristic 1.
Andrew Misseldine Stably Free Modules over the Klein Bottle