  JHK images with angular resolutions approaching the diffraction limit of the
3.6 meter Canada-France-Hawaii Telescope are used to investigate the bright AGB
content of the M31 bulge. The AGB-tip in a field 2.6 arcmin from the galaxy
center occurs at K = 15.6, which is significantly fainter than measured in
previous ground-based studies that sampled similar projected distances from the
center of M31. Within 2.6 arcmin of the center of M31 the number density of
bright AGB stars scales with r-band surface brightness, and the K brightness of
the AGB-tip does not vary measureably with radius. It is concluded that the
infrared bright AGB stars (1) belong to the bulge, and not the disk, and (2)
are well mixed throughout the inner bulge, suggesting that they formed at a
time when the overall structural properties of the M31 bulge were imprinted.
The bolometric luminosity functions of the M31 bulge and Baade's Window are in
excellent agreement, while the brightest AGB stars in the M31 bulge, the
Galactic bulge, and M32 have similar M_K. These data suggest that the brightest
stars in M32 and the bulges of M31 and the Milky-Way belong to an old,
metal-rich population; these stars are bright not because they have a young or
intermediate age, but because they have a high metallicity.
