  In this paper we show that the existence of a non-parabolic local cut point
in the Bowditch boundary $\partial(G,\mathbb{P})$ of a relatively hyperbolic
group $(G,\mathbb{P})$ implies that $G$ splits over a $2$-ended subgroup. This
theorem generalizes a theorem of Bowditch from the setting of hyperbolic groups
to relatively hyperbolic groups. As a consequence we are able to generalize a
theorem of Kapovich and Kleiner by classifying the homeomorphism type of
$1$-dimensional Bowditch boundaries of relatively hyperbolic groups which
satisfy certain properties, such as no splittings over $2$-ended subgroups and
no peripheral splittings.
  In order to prove the boundary classification result we require a notion of
ends of a group which is more general than the standard notion. We show that if
a finitely generated discrete group acts properly and cocompactly on two
generalized Peano continua $X$ and $Y$, then $Ends(X)$ is homeomorphic to
$Ends(Y)$. Thus we propose an alternate definition of $Ends(G)$ which increases
the class of spaces on which $G$ can act.
