  Anomalous topological phases, where edge states coexist with topologically
trivial Chern bands, can only appear in periodically driven lattices. When the
driving is smooth and continuous, the bulk-edge correspondence is guaranteed by
the existence of a bulk invariant known as the winding number. However, in
lattices subject to periodic time-step walks the existence of edge states does
not only depend on bulk invariants but also on the geometry of the boundary.
This is a consequence of the absence of an intrinsic time-dependence or
micromotion in discrete-step walks. We report the observation of edge states
and a simultaneous measurement of the bulk invariants in anomalous topological
phases in a two-dimensional discrete-step walk in a synthetic photonic lattice
made of two coupled fibre rings. The presence of edge states is inherent to the
periodic driving and depends on the geometry of the boundary in the implemented
two-band model with zero Chern number. We provide a suitable expression for the
topological invariants whose calculation does not rely on micromotion dynamics.
