# Asymmetric variety

From Encyclopedia of Mathematics

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.

#### Comments

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

#### References

[Hi] | M.W. Hirsch, "Differential topology", Springer (1976) MR0448362 Zbl 0356.57001 |

**How to Cite This Entry:**

Asymmetric variety.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Asymmetric_variety&oldid=33216

This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article