  We study a link between the ground-state topology and the topology of the
lattice via the presence of anomalous states at disclinations -- topological
lattice defects that violate a rotation symmetry only locally. We first show
the existence of anomalous disclination states, such as Majorana zero-modes or
helical electronic states, in second-order topological phases by means of
Volterra processes. Using the framework of topological crystals to construct
$d$-dimensional crystalline topological phases with rotation and translation
symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous
disclination states from weak and first-order topological phases. We perform
this procedure for all Cartan symmetry classes of topological insulators and
superconductors in two and three dimensions and determine whether the
correspondence between bulk topology, boundary signatures, and disclination
anomaly is unique.
