  Real and complex Clifford bundles and Dirac operators defined on them are
considered. By using the index theorems of Dirac operators, table of
topological invariants is constructed from the Clifford chessboard. Through the
relations between K-theory groups, Grothendieck groups and symmetric spaces,
the periodic table of topological insulators and superconductors is obtained.
This gives the result that the periodic table of real and complex topological
phases is originated from the Clifford chessboard and index theorems.
