antipodal
Definition Suppose and are points on the -sphere (http://planetmath.org/Sphere) . If then and are called antipodal points. The antipodal map is the map defined as .
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1.
The antipodal map is homotopic (http://planetmath.org/HomotopyOfMaps) to the identity map if is odd [1].
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2.
The degree (http://planetmath.org/DegreeMapOfSpheres) of the antipodal map is .
References
- 1 V. Guillemin, A. Pollack, Differential topology, Prentice-Hall Inc., 1974.
Title | antipodal |
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Canonical name | Antipodal |
Date of creation | 2013-03-22 13:57:45 |
Last modified on | 2013-03-22 13:57:45 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 6 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 51M05 |
Classification | msc 15-00 |
Related topic | DiametralPoints |
Defines | antipodal points |
Defines | antipodal map |