Stably Free Modules over the Klein Bottle
Stably Free Modules over the Klein Bottle
Stably Free Modules over the Klein Bottle
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Introduction<br />
Constructing a <strong>Stably</strong> <strong>Free</strong> Module<br />
Applications to <strong>the</strong> <strong>Klein</strong> <strong>Bottle</strong><br />
The Ring ZG<br />
In light of <strong>the</strong> presentation of G,<br />
ZG = Z[y, y −1 ][x, x −1 ; σ]<br />
and σ is <strong>the</strong> isomorphism induced by<br />
In particular,<br />
as polynomials in Z[y, y −1 ].<br />
σ : y ↦−→ y −1 .<br />
yn = ny, ∀n ∈ Z<br />
Andrew Misseldine <strong>Stably</strong> <strong>Free</strong> <strong>Modules</strong> <strong>over</strong> <strong>the</strong> <strong>Klein</strong> <strong>Bottle</strong>