Asymmetric variety

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An oriented variety $M$ without an orientation-reversing homeomorphism. Thus, for instance, the complex projective plane is an asymmetric variety, since the self-intersection of the complex straight line is $+1$ or $-1$, depending on the orientation. Certain knots can differ from their mirror image owing to the fact that their branched coverings are asymmetric varieties.


This notion can be found, e.g., in [Hi], Chapt. 5.


[Hi] M.W. Hirsch, "Differential topology", Springer (1976) MR0448362 Zbl 0356.57001
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Asymmetric variety. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article