Y-homeomorphism

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 formula_1 has no y-homeomorphism. 