18.41 (2014)

Let $F$ be a free group of rank 2.
$\qquad$ a) It is known that $\text{scl}(g) = 0$ only for $g = 1$, and $\text{scl}(g) \geqslant 1/2$ for all $1 \neq g \in [F, F]$. Is 1/2 an isolated value?
$\qquad$ b) Are there any intervals $J$ in $\mathbb{R}$ such that the set of values of $\text{scl}$ on $[F, F]$ is dense in $J$?
$\qquad$ c) Is there some $T \in \mathbb{R}$ such that every rational number $\geqslant T$ is a value of $\text{scl}(g)$ for $g \in [F, F]$?