and if not then where is free abelian, and the factor is generated by the middle curve in a Möbius band embedded in .

Orientability of manifolds

Let M be a connected topological n-manifold. There are several possible definitions of what it means for M to be orientable. Some of these definitions require that M has extra structure, like being differentiable. Occasionally, must be made into a special case. When more than one of

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