  In this paper we provide a classification theorem for 1-dimensional
boundaries of groups with isolated flats. Given a group $\Gamma$ acting
geometrically on a $CAT(0)$ space $X$ with isolated flats and 1-dimensional
boundary, we show that if $\Gamma$ does not split over a virtually cyclic
subgroup, then $\partial X$ is homeomorphic to a circle, a Sierpinski carpet,
or a Menger curve. This theorem generalizes a theorem of Kapovich-Kleiner, and
resolves a question due to Kim Ruane.
  We also study the relationship between local cut points in $\partial X$ and
splittings of $\Gamma$ over $2$-ended subgroups. In particular, we generalize a
theorem of Bowditch by showing that the existence of a local point in $\partial
X$ implies that $\Gamma$ splits over a $2$-ended subgroup.
