What is "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 ${\mathbb RP}^2$ has no y-homeomorphism.