Difference between revisions of "Desorienting path"
From Encyclopedia of Mathematics
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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 | + | {{TEX|done}} |
| + | 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. | ||
Latest revision as of 20:12, 11 April 2014
A closed path on a manifold, the traversal of which involves a change in the sign of the local orientation (cf. Orientation of a manifold). Desorienting paths exist only on a non-oriented manifold $M$, and a homomorphism from the fundamental group $\pi_1(M)$ onto $\mathbf Z_2$ with kernel consisting of classes of loops which are not desorienting paths is unambiguously defined.
How to Cite This Entry:
Desorienting path. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Desorienting_path&oldid=31556
Desorienting path. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Desorienting_path&oldid=31556
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article