  Modeling the spin-triplet superconductor Sr2RuO4 through a three-orbital
tight-binding model we investigate topological properties and edge states
assuming chiral p-wave pairing. In concordance with experiments the three Fermi
surfaces consist of two electron-like and one hole-like one corresponding to
the alpha-, beta- and gamma-band on the level of a two-dimensional system. The
quasi-particle spectra and other physical quantities of the superconducting
phase are calculated by means of a self-consistent Bogoliubov-de Gennes
approach for a ribbon shaped system. While a full quasiparticle excitation gap
is realized in the bulk system, at the edges gapless states appear some of
which have linear and others nearly flat dispersion around zero energy. This
study shows the interplay between spin-orbit coupling induced spin currents,
chiral edge currents and correlation driven surface magnetism. The topological
nature of the chiral p-wave state manifests itself in the gamma-band
characterized by an integer Chern number. As the gamma-band is close to a
Lifshitz transition in Sr2RuO4, changing the sign of the Chern number, the
topological nature may be rather fragile.
