We study the coherent light-matter interactions of GaAs quantum wells associated with excitons, biexcitons and many-body effects. For most polarization configurations, excitonic features dominate the phase-resolved two-dimensional Fourier-transform (2DFT) spectra and have dispersive lineshapes, indicating the presence of many-body interactions. For cross-linear excitation, excitonic features become weak and absorptive due to the strong suppression of many-body effects; a result that can not be directly determined in transient four-wave mixing experiments. The biexcitonic features do not weaken for cross-polarized excitation and thus are more important.
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