  We theoretically study topological laser operation in a bosonic
Harper-Hofstadter model featuring a saturable optical gain. Crucial
consequences of the chirality of the lasing edge modes are highlighted, such as
a sharp dependence of the lasing threshold on the geometrical shape of the
amplifying region and the possibility of ultraslow relaxation times and of
convectively unstable regimes. The different unstable regimes are characterized
in terms of spatio-temporal structures sustained by noise and a strong
amplification of a propagating probe beam is anticipated to occur in between
the convective and the absolute (lasing) thresholds. The robustness of
topological laser operation against static disorder is assessed.
