  IceCube-Gen2, the extension of the IceCube Neutrino Observatory, will feature
three main components: an optical array in the deep ice, a large-scale radio
array in the shallow ice and firn, and a surface detector above the optical
array. Thus, IceCube-Gen2 will not only be an excellent detector for PeV
neutrinos, but also constitutes a unique setup for the measurement of
cosmic-ray air showers, where the electromagnetic component and low-energy
muons are measured at the surface and high-energy muons are measured in the
ice. As for ongoing enhancement of IceCube's current surface array, IceTop, we
foresee a combination of elevated scintillation and radio detectors for the
Gen2 surface array, aiming at high measurement accuracy for air showers. The
science goals are manifold: The in-situ measurement of the cosmic-ray flux and
mass composition, as well as more thorough tests of hadronic interaction
models, will improve the understanding of muons and atmospheric neutrinos
detected in the ice, in particular, regarding prompt muons. Moreover, the
surface array provides a cosmic-ray veto for the in-ice detector and
contributes to the calibration of the optical and radio arrays. Last but not
least, the surface array will make major contributions to cosmic-ray science in
the energy range of the transition from Galactic to extragalactic sources. The
increased sensitivities for photons and for cosmic-ray anisotropies at
multi-PeV energies provide a chance to solve the puzzle of the origin of the
most energetic Galactic cosmic rays and will serve IceCube's multimessenger
mission.
