Let $F:\mathbb{C}^n\to \mathbb{C}^n$ be a homeomorphism homogeneous of degree 1 (i.e., $F(tx)=tF(x)$, $t>0$) and $g:\mathbb{C}^n\to \mathbb{C}$ a homogeneous polynomial of degree $k$. Let $L$ ($0\in L$) a complex line and $H=F(L)$. It is true that $h=g|_H\circ F|_L$ has topological degree less than or equal to k? This is true if F is linear map!

Let $F:\mathbb{C}\to \mathbb{C}$ be a homogeneous map of degree $k$ (i.e., $F(tx)=t^kF(x)$, $t>0$). It is true that $F$ has topological degree less than or equal to k? This is true if F is polynomial!

Let $F:\mathbb{R}^2\to \mathbb{R}^2$ be a homogeneous function of degree $k\in \mathbb{Z}_+$ (i.e., $F(tx)=t^kF(x)$, $t>0$) such that $F^{-1}(\{0\}) = (0)$. It is true that F has topological degree less than or equal to k? This is true if F is homogeneous polynomial!

Let $F:\mathbb{C}^n\to \mathbb{C}^n$ be a homeomorphism homogeneous of degree 1 (i.e., $F(tx)=tF(x)$, $t>0$) and $g:\mathbb{C}^n\to \mathbb{C}$ a homogeneous polynomial of degree $k$. Let $L$ ($0\in L$) a complex line and $H=F(L)$. It is true that $h=g|_H\circ F|_L$ has topological degree less than or equal to k? This is true if F is linear map!

Let $F:\mathbb{R}^2\to \mathbb{R}^2$ be a homogeneous function of degree $k\in \mathbb{Z}_+$ (i.e., $F(tx)=t^kF(x)$, $t>0$) such that $F^{-1}(\{0\}) = (0)$. It is true that F has topological degree less than or equal to k? This is true if F is homogeneous polynomial!

Let $F:\mathbb{R}^2\to \mathbb{R}^2$ be a homogeneous function of degree $k\in \mathbb{Z}_+$ (i.e., $F(tx)=t^kF(x)$, $t>0$) such that $F^{-1}(\{0\}) = (0)$. It is true that F has topological degree less than or equal to k? This is true if F is homogeneous polynomial!