## You are here

Homeantipodal

## Primary tabs

# antipodal

Definition Suppose $x$ and $y$ are points on the $n$-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. The antipodal map$A:S^{n}\to S^{n}$ is homotopic to the identity map if $n$ is odd [1].

2. The degree of the antipodal map is $(-1)^{{n+1}}$.

# References

- 1
V. Guillemin, A. Pollack,
*Differential topology*, Prentice-Hall Inc., 1974.

Defines:

antipodal points, antipodal map

Related:

DiametralPoints

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

51M05*no label found*15-00

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Sep 17

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella