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- Orientability abstract "In mathematics, orientability is a property of surfaces in Euclidean space measuring 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 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 .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.".
- Orientability thumbnail Torus.png?width=300.
- Orientability wikiPageExternalLink Orientation.
- Orientability wikiPageExternalLink Orientation_covering.
- Orientability wikiPageExternalLink Orientation_of_manifolds.
- Orientability wikiPageExternalLink Orientation_of_manifolds_in_generalized_cohomology_theories.
- Orientability wikiPageID "187446".
- Orientability wikiPageRevisionID "603808441".
- Orientability hasPhotoCollection Orientability.
- Orientability subject Category:Differential_topology.
- Orientability subject Category:Surfaces.
- Orientability type Artifact100021939.
- Orientability type Object100002684.
- Orientability type PhysicalEntity100001930.
- Orientability type Surface104362025.
- Orientability type Surfaces.
- Orientability type Whole100003553.
- Orientability comment "In mathematics, orientability is a property of surfaces in Euclidean space measuring 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.".
- Orientability label "Orientabilidade".
- Orientability label "Orientability".
- Orientability label "Oriënteerbaarheid".
- Orientability label "可定向性".
- Orientability label "向き付け可能性".
- Orientability sameAs 向き付け可能性.
- Orientability sameAs 방향_(다양체).
- Orientability sameAs Oriënteerbaarheid.
- Orientability sameAs Orientabilidade.
- Orientability sameAs m.019mzr.
- Orientability sameAs Q2748415.
- Orientability sameAs Q2748415.
- Orientability sameAs Orientability.
- Orientability wasDerivedFrom Orientability?oldid=603808441.
- Orientability depiction Torus.png.
- Orientability isPrimaryTopicOf Orientability.
