  We recently found extended CO(2-1) emission from cold molecular gas embedded
in the network of Halpha filaments surrounding the galaxy NGC 1275 (Salome et
al. 2006). We now present CO(2-1) interferometer maps of the eastern filaments,
at high spatial and spectral resolutions. The cold molecular gas is detected by
the Plateau de Bure Interferometer along the eastern filaments over an extent
of 15'', or with a projected length of 5kpc. In our 2.5'' beam, the main CO
filament is mostly unresolved along its minor axis. The multiple peaks along
the CO filaments and the low values of the observed CO brightness temperatures
imply further unresolved structures that may be giant molecular clouds. These
clouds have very narrow line-width emission lines (~30 km/s). The CO emission
is optically thick. It very likely traces cold clouds bound under their own
self-gravity that may be falling back in the gravitational potential well of
the galaxy. Such a picture would agree with current models of ``positive
feedback'' in which some of the hot gas around NGC 1275 (a) is trapped by
buoyantly rising bubbles inflated by the energy input of the 3C84 AGN, (b)
subsequently cools efficiently at a larger radius around the edges of the hot
bubbles, and (c) then falls back in self-gravitating clouds of molecular gas
toward the center of the galaxy.
