  We study the band-edge exciton fine structure and in particular its
bright-dark splitting in colloidal semiconductor nanocrystals by four different
optical methods based on fluorescence line narrowing and time-resolved
measurements at various temperatures down to 2 K. We demonstrate that all these
methods provide consistent splitting values and discuss their advances and
limitations. Colloidal CdSe nanoplatelets with thicknesses of 3, 4 and 5
monolayers are chosen for experimental demonstrations. The bright-dark
splitting of excitons varies from 3.2 to 6.0 meV and is inversely proportional
to the nanoplatelet thickness. Good agreement between experimental and
theoretically calculated size dependence of the bright-dark exciton slitting is
achieved. The recombination rates of the bright and dark excitons and the
bright to dark relaxation rate are measured by time-resolved techniques.
