  A topological argument is presented for nodal structures of superconducting
states with time-reversal invariance. A generic Hamiltonian which describes a
quasiparticle in superconducting states with time-reversal invariance is
derived, and it is shown that only line nodes are topologically stable in
single-band descriptions of superconductivity. Using the time-reversal
symmetry, we introduce a real structure and define topological numbers of line
nodes. Stability of line nodes is ensured by conservation of the topological
numbers. Line nodes in high-Tc materials, the polar state in p-wave paring and
mixed singlet-triplet superconducting states are examined in detail.
