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.

See also

• Lickorish-Wallace theorem

References

• J. S. Birman, D. R. J. Chillingworth, On the homeotopy group of a non-orientable surface, Trans. Amer. Math. Soc. 247 (1979), 87-124.
• 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.
• M. Korkmaz, Mapping class group of non-orientable surface, Geometriae Dedicata 89 (2002), 109-133.
• W. B. R. Lickorish, Homeomorphisms of non-orientable two-manifolds, Math. Proc. Camb. Phil. Soc. 59 (1963), 307-317.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometric topology Homeomorphisms Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат EPresence Interactive Media Issay Dobrowen Look at other dictionaries: homeomorphism — homeomorphism. См. гомеоморфизм. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь. homeomorphism — 1854, from homeomorphous (1832), from HOMEO (Cf. homeo ) + morphous (see METAMORPHOSIS (Cf. metamorphosis)); originally of crystals. Homeomorphic is from 1902 …   Etymology dictionary homeomorphism — [hō΄mē ō môr′fiz΄əm] n. [ HOMEO + MORPH + ISM] similarity in structure and form; esp., a close similarity of crystalline forms between substances of different chemical composition homeomorphous [hō΄mē ō΄môr′fəs] adj …   English World dictionary Homeomorphism — Topological equivalence redirects here; see also topological equivalence (dynamical systems). donut illustrating that they are homeomorphic. But there does not need to be a continuous deformation for two spaces to be homeomorphic.In the… …   Wikipedia homeomorphism — homeomorphic, homeomorphous, adj. /hoh mee euh mawr fiz euhm/, n. 1. similarity in crystalline form but not necessarily in chemical composition. 2. Math. a function between two topological spaces that is continuous, one to one, and onto, and the… …   Universalium homeomorphism — noun Etymology: International Scientific Vocabulary Date: 1854 a function that is a one to one mapping between sets such that both the function and its inverse are continuous and that in topology exists for geometric figures which can be… …   New Collegiate Dictionary Homeomorphism (graph theory) — In graph theory, two graphs G and G are homeomorphic if there is an isomorphism from some subdivision of G to some subdivision of G . If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted… …   Wikipedia homeomorphism — noun a) a continuous bijection from one topological space to another, with continuous inverse. b) a similarity in the crystal structure of unrelated compounds …   Wiktionary homeomorphism — [ˌhɒmɪə(ʊ) mɔ:fɪz(ə)m, ˌhəʊm ] noun Mathematics an instance of topological equivalence. Derivatives homeomorphic adjective Origin from Gk homoios like + morphē form + ism …   English new terms dictionary homeomorphism — ho·meo·mor·phism …   English syllables homeomorphism — ho•me•o•mor•phism [[t]ˌhoʊ mi əˈmɔr fɪz əm[/t]] n. math. a mathematical function between two topological spaces that is continuous, one to one, and onto, and the inverse of which is continuous • Etymology: 1850–55 ho me•o•mor′phic, ho… …   From formal English to slang 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”