  We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners
and propose a periodic table for topological invariants related to corner
states aimed at studies of higher-order topological insulators. Our table is
based on four things: (1) the definition of topological invariants, (2) a proof
of their relation with corner states (3) computations of K-groups and (4) a
construction of explicit examples.
