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|
Asymmetric variety. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Asymmetric_variety&oldid=33216