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Asymmetric variety

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MathematicsTopologyTopological StructuresReal 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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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=53857

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

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Real Projective PlaneMathematics / Topology / Topological Structures / Real Projective Planemethod: title_similarity - confidence: 0.90suggested

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Asymmetric varietyencyclopedia_of_mathematics

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Homeomorphismoutgoing citation Projective planeoutgoing citation

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discussesarticle:eom--asymmetric-variety--3f5e761a4e -> concept:asymmetric-varietyconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:asymmetric-variety -> concept:homeomorphismconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:asymmetric-variety -> concept:projective-planeconfidence: 1.00 - provenance: article link extractionreviewed

subcategory_ofconcept:asymmetric-variety -> topic:real-projective-planeconfidence: 0.90 - provenance: title_similarity classificationsuggested

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