A note on topological invariants in condensed matter

We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time reversal invariant or if there are more phases that has different topological invariants. From a mathematical point of view may exist more topological phases of matter as a subclass of one well established phase.
Comment: revised version with some misprints corrected