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

Let G=SO(m+1)$G=SO(m+1)$ , m \geq 2$m \geq 2$, act in the standard way on S^m$S^m$.

Let F:S^m \to S^m$F:S^m \to S^m$ be a G$G$-equivariant map, i.e., g F(g^{-1}x) =F(x)$g F(g^{-1}x) =F(x)$ for all x \in S^m$x \in S^m$ and g \in G$g \in G$.

Question 1: Is F the identity map?

Question 1: Is F the identity map?

If the answer is negative: Is F$F$ an isometry?

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 identity map?

If the answer is negative: Is F an isometry?

$SO(m+1)$-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 identity map?

If the answer is negative: Is $F$ an isometry?

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Andrea Ratto
Andrea Ratto
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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 identity map?

If the answer is negative: Is F an isometry?