# antipodal

Definition Suppose $x$ and $y$ are points on the $n$-sphere (http://planetmath.org/Sphere) $S^{n}$. If $x=-y$ then $x$ and $y$ are called antipodal points. The antipodal map is the map $A:S^{n}\to S^{n}$ defined as $A(x)=-x$.

Properties

1. 1.

The antipodal map$A:S^{n}\to S^{n}$ is homotopic (http://planetmath.org/HomotopyOfMaps) to the identity map if $n$ is odd [1].

2. 2.

The degree (http://planetmath.org/DegreeMapOfSpheres) of the antipodal map is $(-1)^{n+1}$.

## References

Title antipodal Antipodal 2013-03-22 13:57:45 2013-03-22 13:57:45 mathcam (2727) mathcam (2727) 6 mathcam (2727) Definition msc 51M05 msc 15-00 DiametralPoints antipodal points antipodal map