Definition Suppose x and y are points on the n-sphere ( Sn. If x=-y then x and y are called antipodal points. The antipodal map is the map A:SnSn defined as A(x)=-x.


  1. 1.

    The antipodal mapA:SnSn is homotopic ( to the identity map if n is odd [1].

  2. 2.

    The degree ( of the antipodal map is (-1)n+1.


Title antipodal
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