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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

6 votes
3 answers
325 views

$SO(m+1)$-equivariant maps from $S^m$ to $S^m$

Let $G=SO(m+1)$ , $m \geq 2$, act in the standard way on $S^m$. Let $F:S^m \to S^m$ be a $G$-equivariant map, i.e., $g F(g^{-1}x) =F(x)$ for all $x \in S^m$ and $g \in G$. Question 1: Is F the id …
Andrea Ratto's user avatar