  We present a detailed study of the gap symmetry and the quasiparticle wave
function topology in two-dimensional superconductors without inversion center.
The strong spin-orbit coupling of electrons with the crystal lattice makes it
necessary to describe superconductivity in terms of one or more nondegenerate
bands characterized by helicity. We develop a topological classification of the
superconducting states using the integer-valued Maurer-Cartan invariants and
the Bogoliubov Wilson loops, and also calculate the spectrum of fermionic
boundary modes.
