  Luminous compact blue galaxies (LCBGs) are a diverse class of galaxies
characterized by high luminosity, blue color, and high surface brightness that
sit at the critical juncture of galaxies evolving from the blue to the red
sequence. As part of our multi-wavelength survey of local LCBGs, we have been
studying the HI content of these galaxies using both single-dish telescopes and
interferometers. Our goals are to determine if single-dish HI observations
represent a true measure of the dynamical mass of LCBGs and to look for
signatures of recent interactions that may be triggering star formation in
LCBGs. Our data show that while some LCBGs are undergoing interactions, many
appear isolated. While all LCBGs contain HI and show signatures of rotation,
the population does not lie on the Tully-Fisher relation nor can it evolve onto
it. Furthermore, the HI maps of many LCBGs show signatures of dynamically hot
components, suggesting that we are seeing the formation of a thick disk or
spheroid in at least some LCBGs. There is good agreement between the HI and
H-alpha kinematics for LCBGs, and both are similar in appearance to the H-alpha
kinematics of high redshift star-forming galaxies. Our combined data suggest
that star formation in LCBGs is primarily quenched by virial heating,
consistent with model predictions.
