Geometric group theory
Linear metric on F2, free group with two generator.
I may have made a stupid mistake, but if not, we could construct a metric by pullback a metric on a suitable linear normalized space $latex H$ which we carefully constructed. Let we define the generators of free group $latex F_2$ by $latex a,b$. Step 1. Constructed the linear normalized space $latex H$. the space $latex H$ was spanned by basis $latex \Lambda=\Lambda_a \coprod \Lambda_b$, $latex \Lambda_a, \Lambda_b$ are defined by look at the Cayley graph of $latex F_2$, there is a lot of vertic…