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- Q2748415 subject Q7139288.
- Q2748415 subject Q8266666.
- Q2748415 subject Q8802316.
- Q2748415 abstract "Template:ForIn mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance. More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is orientable if a two-dimensional figure such as 20px in the space cannot be moved (continuously) around the space and back to where it started so that it looks like its own mirror image 20px.The notion of orientability can be generalised to higher-dimensional manifolds as well. A manifold is orientable if it has a consistent choice of orientation, and a connected orientable manifold has exactly two different possible orientations. In this setting, various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.".
- Q2748415 thumbnail Torus.png?width=300.
- Q2748415 wikiPageExternalLink Orientation.
- Q2748415 wikiPageExternalLink Orientation_covering.
- Q2748415 wikiPageExternalLink Orientation_of_manifolds.
- Q2748415 wikiPageExternalLink Orientation_of_manifolds_in_generalized_cohomology_theories.
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- Q2748415 wikiPageWikiLink Q8802316.
- Q2748415 type Thing.
- Q2748415 comment "Template:ForIn mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance.".
- Q2748415 label "Orientability".
- Q2748415 seeAlso Q2193452.
- Q2748415 depiction Torus.png.