For example, let " X " be an oriented manifold, not necessarily compact.
2.
For "'CP "'2 this process ought to produce an oriented manifold.
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Two oriented manifolds are oriented cobordant if and only if their Stiefel Whitney and Pontrjagin numbers are the same.
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This is similar to the cobordism ring of oriented manifolds, except that the manifolds also have a vector bundle.
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For non-oriented manifolds the easiest way to state a geometrization conjecture is to first take the oriented double cover.
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On an oriented manifold, the proportionality of any two volume forms can be thought of as a geometric form of the Radon Nikodym theorem.
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If the moduli space is a smooth, compact, oriented manifold or orbifold, then the integration ( or a fundamental class ) can be defined.
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On an orientable but not oriented manifold, there are two choices of orientation; either choice allows one to integrate-forms over compact subsets, with the two choices differing by a sign.
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Where ? ( d ) is closed ( i . e . without boundary ) and oriented, then it is the boundary of some d + 1 dimensional oriented manifold M d + 1.
10.
Let M _ 1 and M _ 2 be two smooth, oriented manifolds of equal dimension and V a smooth, closed, oriented manifold, embedded as a submanifold into both M _ 1 and M _ 2.
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