Difference between revisions of "Asymmetric variety"
From Encyclopedia of Mathematics
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| − | An oriented variety | + | {{TEX|done}} |
| − | + | 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. | |
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====Comments==== | ====Comments==== | ||
| − | This notion can be found, e.g., in | + | This notion can be found, e.g., in {{Cite|Hi}}, Chapt. 5. |
====References==== | ====References==== | ||
| − | + | * {{Ref|Hi}} M.W. Hirsch, "Differential topology", Springer (1976) {{MR|0448362}} {{ZBL|0356.57001}} | |
Latest revision as of 06:09, 23 April 2023
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=14204
Asymmetric variety. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Asymmetric_variety&oldid=14204
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article