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 />
This is a <strong>Klein</strong> <strong>Bottle</strong><br />
x ❄<br />
•<br />
v0<br />
✲ y<br />
✛<br />
y<br />
We see from <strong>the</strong> fundamental square, that<br />
Call this group G.<br />
X<br />
x<br />
❄<br />
π(X , v0) = 〈x, y | x −1 yx = y −1 〉<br />
= 〈x, y | yx = xy −1 〉<br />
Andrew Misseldine <strong>Stably</strong> <strong>Free</strong> <strong>Modules</strong> <strong>over</strong> <strong>the</strong> <strong>Klein</strong> <strong>Bottle</strong>