  Topological crystalline phases (TCPs) are topological states protected by
spatial symmetries. A broad range of TCPs have been conventionally studied by
formulating topological invariants (symmetry indicators) at invariant momenta
in the Brillouin zone, which leaves open the question of their stability in the
absence of translational invariance. In this work, we show that robust
basis-independent topological invariants can be generically constructed for
TCPs using projected symmetry operators. Remarkably we show that the real-space
topological markers of these invariants are exponentially localized to the
fixed points of the spatial symmetry. As a result, this real-space structure
protects them against the presence of impurities that are located away from the
fixed points. By considering all possible symmetry centers in a crystalline
system we can generate a mesh of real-space topological markers that can
provide a local topological distinction for TCPs. We illustrate the robustness
of this mesh of invariants with 1D and 2D TCPs protected by inversion,
rotational and mirror symmetries. Finally, we find that the boundary modes of
these TCPs can also exhibit robust topological invariants with localized
markers on the edges. We illustrate this with the gapless Majorana boundary
modes of mirror-symmetric topological superconductors, and relate their integer
topological edge invariant with a quantized effective edge polarization.
