For example, let " X " be an oriented manifold, not necessarily compact.
2.
For "'CP "'2 this process ought to produce an oriented manifold.
3.
Two oriented manifolds are oriented cobordant if and only if their Stiefel Whitney and Pontrjagin numbers are the same.
4.
This is similar to the cobordism ring of oriented manifolds, except that the manifolds also have a vector bundle.
5.
For non-oriented manifolds the easiest way to state a geometrization conjecture is to first take the oriented double cover.
6.
On an oriented manifold, the proportionality of any two volume forms can be thought of as a geometric form of the Radon Nikodym theorem.
7.
If the moduli space is a smooth, compact, oriented manifold or orbifold, then the integration ( or a fundamental class ) can be defined.
8.
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.
9.
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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