  We derive a general relation between the stacking vector ${\bf u}$ describing
the relative shift of two layers of bilayer graphene and the Chern index. We
find $C = \nu - \text{sign}\left(|V_{AB}|-|V_{BA}|\right)$, where $\nu$ is a
valley index and $|V_{\alpha\beta}|$ the absolute value of stacking potentials
that depend on ${\bf u}$ and that uniquely determine the interlayer
interaction; AA stacking plays no role in the topological character. With this
expression we show that while ideal and relaxed minimally twisted bilayer
graphene appear so distinct as to be almost different materials, their Chern
index maps are, remarkably, identical. The topological physics of this material
is thus strongly robust to lattice relaxations.
