Orientability

:This article discusses orientability and orientation on surfaces and manifolds. For orientation of vector spaces see orientation (mathematics). For alternate uses, see orientation.

Orientation and vector bundles

A real vector bundle, which a priori has a GL(n) structure group, is called orientable when the structure group may be reduced to GL^{+}(n), the group of matrices with positive determinant. A smooth real manifold is orientable if and only if its tangent bundle is.

Related Topics:
Vector bundle - GL(n) - Structure group - Matrices - Determinant - Smooth - Manifold - Tangent bundle

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