orientability sentence in Hindi
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- If is a compact orientable-dimensional manifold, then embeds in ( for not a power of 2 the orientability condition is superfluous ).
- Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.
- Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal 4-polytopes, and this led to the use of torsion coefficients.
- (note the final B _ n is missing the superscript " 1; this flip, as compared to the orientable case, being the source of the non-orientability ).
- Weeks doesn't discuss the implications, if any, of non-orientability, i . e . the existence of closed paths in space such that a traveler comes back with reversed chirality.
- More concretely, triviality of the determinant bundle \ Omega ^ n ( M ) is equivalent to orientability, and a line bundle is trivial if and only if it has a nowhere-vanishing section.
- Conversely, if " M " is orientable, then local volume forms can be patched together to create a global volume form, orientability being necessary to ensure that the global form is nowhere vanishing.
- These homology classes agree on chart overlaps because of the orientability of the atlas, so they may be patched together to get a class in H _ n ( M; \ mathbf { Z } ).
- Two smooth surfaces are diffeomorphic if and only if they are homeomorphic . ( The analogous result does not hold for higher-dimensional manifolds . ) Thus closed surfaces are classified up to diffeomorphism by their Euler characteristic and orientability.
- Two smooth surfaces are diffeomorphic if and only if they are homeomorphic . ( The analogous result does not hold for manifolds of dimension greater than three . ) It follows that closed surfaces are classified up to diffeomorphism by their Euler characteristic and orientability.
- :Correction : " no distinction between inside and outside " means, according to the orientability article, that an " ant " crawling on one side at a particular spot can get to the other side of that same spot without leaving the surface or flipping over an edge.
- 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.
- 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.
- The significance of this construction begins with the following result, which belongs to the subject of cohomology of fiber bundles . ( We have stated the result in terms of "'Z "'2 coefficients to avoid complications arising from orientability; see also Orientation of a vector bundle # Thom space .)
- One feature of the bundle of densities ( again assuming orientability ) " L " is that " L " " s " is well-defined for real number values of " s "; this can be read from the transition functions, which take strictly positive real values.
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