Show that \(S^n\) has a continuous field of nonzero tangent vectors iff \(n>0\) is odd. Conclude that the even-dimensional spheres are not Lie groups.
Question
Math 6510 • Differentiable Manifolds
Spring 2017 • Question 9
Question
Spring 2017 • Question 9
Show that \(S^n\) has a continuous field of nonzero tangent vectors iff \(n>0\) is odd. Conclude that the even-dimensional spheres are not Lie groups.