crosscap slide

The crosscap slide is an autohomeomorphism which can be defined only for non orientable surfaces whose genus is greater than one.

It is also known as the y-homeomorphism. This name was coined by Lickorish and the name crosscap slide was introduced by Korkmaz.

1.

D.R.J. Chillingworth. A finite set of generators for the homeotopy group of a non-orientable surface, Proc. Camb. Phil. Soc. 65(1969), 409-430.
2.

M. Korkmaz. Mapping Class Groups of Non-orientable Surfaces, Geometriae Dedicata 89 (2002), 109-133.
3.

W.B.R. Lickorish. Homeomorphisms of non-orientable two-manifolds, Math. Proc. Camb. Phil. Soc. 59 (1963), 307-317.