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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the y-homeomorphism, or crosscap slide, is a special type of auto-homeomorphism in non-orientable surfaces. It can be constructed by sliding a Möbius band included on the surface around an essential 1-sided closed curve until the original position; thus it is necessary that the surfaces have genus greater than one. The projective plane {RP}2 has no y-homeomorphism.