Motivated by the recent result that left-orderability of a group
is intimately connected to circular orderability of direct products
, we
provide necessary and sufficient cohomological conditions that such a direct
product be circularly orderable. As a consequence of the main theorem, we
arrive at a new characterization for the fundamental group of a rational
homology 3-sphere to be left-orderable. Our results imply that for mapping
class groups of once-punctured surfaces, and other groups whose actions
on are cohomologically
rigid, the products
are seldom circularly orderable. We also address circular orderability of direct
products in general, dealing with the cases of factor groups admitting a
biinvariant circular ordering and iterated direct products whose factor groups are
amenable.
