Cross hood

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A cross-cap or tree cap refers to a specific area in the mathematics .

Taken on its own, the cross hood is equivalent to a projective plane . In general, however, the term refers to a correspondingly shaped part of a larger manifold , whereby the edge of a Möbius strip is connected to an opening in the manifold, so that no edge remains. In this form, the cross hood can no longer be embedded in the three-dimensional space without self-penetration . Most representations of a cross hood show it on the surface of a sphere .

The property that the cross hood cannot be oriented is carried over to the associated variety .

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