y-homeomorphism
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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 strip 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 has no y-homeomorphism.
See also
References
- {{cite journal
| last1=Birman | first1=J. S. | authorlink1=Joan Birman
| last2=Chillingworth | first2=D. R. J.
| title=On the homeotopy group of a non-orientable surface
| journal=Mathematical Proceedings of the Cambridge Philosophical Society
| volume=71
| issue=3
| date=1972
| pages=437–448
| doi=10.1017/S0305004100050714| bibcode=1972PCPS...71..437B }}
- {{cite journal
| last1=Chillingworth | first1=D. R. J.
| title=A finite set of generators for the homeotopy group of a non-orientable surface
| journal=Mathematical Proceedings of the Cambridge Philosophical Society
| volume=65
| issue=2
| date=1969
| pages=409–430
| doi=10.1017/S0305004100044388| bibcode=1969PCPS...65..409C
}}
- {{cite journal
| last1=Korkmaz | first1=Mustafa
| title=Mapping class group of non-orientable surface
| journal=Geometriae Dedicata
| volume=89
| date=2002
| pages=109–133
| doi=10.1023/A:1014289127999}}
- {{cite journal
| last1=Lickorish | first1=W. B. R. | authorlink1=W. B. R. Lickorish
| title=Homeomorphisms of non-orientable two-manifolds
| journal=Mathematical Proceedings of the Cambridge Philosophical Society
| volume=59
| issue=2
| date=1963
| pages=307–317
| doi=10.1017/S0305004100036926| bibcode=1963PCPS...59..307L }}
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