  For $A$ a gentle algebra, and $X$ and $Y$ string modules, we construct a
combinatorial basis for Hom($X,\tau Y$). We use this to describe support
$\tau$-tilting modules for $A$. We give a combinatorial realization of maps in
both directions realizing the bijection between support $\tau$-tilting modules
and functorially finite torsion classes. We give an explicit basis of
Ext$^1(Y,X)$ as short exact sequences. We analyze several constructions given
in a more restricted, combinatorial setting by McConville, showing that many
but not all of them can be extended to general gentle algebras.
