View source for Desorienting path

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A closed path on a manifold, the traversal of which involves a change in the sign of the local orientation (cf. [[Orientation|Orientation]] of a manifold). Desorienting paths exist only on a non-oriented manifold $M$, and a homomorphism from the [[Fundamental group|fundamental group]] $\pi_1(M)$ onto $\mathbf Z_2$ with kernel consisting of classes of loops which are not desorienting paths is unambiguously defined.