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Orientation double cover of the Klein bottle

For

(x, y) ≃ (x + c, (- 1)^{c} y + d),

the transformations with even

c

form an index-two translation subgroup. Its quotient is a torus, giving the orientation double cover

T^{2} \to K

.

Table of contents 80 1
- Klein-bottle mapping-cylinder obstruction to simple connectivity Orientation double cover of the Klein bottle 55

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