  We show that collisions with stellar--mass black holes can partially explain
the absence of bright giant stars in the Galactic Centre, first noted by Genzel
et al, 1996. We show that the missing objects are low--mass giants and AGB
stars in the range 1-3 M$_{\odot}$. Using detailed stellar evolution
calculations, we find that to prevent these objects from evolving to become
visible in the depleted K bands, we require that they suffer collisions on the
red giant branch, and we calculate the fractional envelope mass losses
required. Using a combination of Smoothed Particle Hydrodynamic calculations,
restricted three--body analysis and Monte Carlo simulations, we compute the
expected collision rates between giants and black holes, and between giants and
main--sequence stars in the Galactic Centre. We show that collisions can
plausibly explain the missing giants in the $10.5<K<12$ band. However,
depleting the brighter ($K<10.5$) objects out to the required radius would
require a large population of black hole impactors which would in turn deplete
the $10.5<K<12$ giants in a region much larger than is observed. We conclude
that collisions with stellar--mass black holes cannot account for the depletion
of the very brightest giants, and we use our results to place limits on the
population of stellar--mass black holes in the Galactic Centre.

Astrophysics