  We evaluate the dry merger activity in the Coma cluster, using a
spectroscopically complete sample of 70 red-sequence (RS) galaxies, most of
which (~75%) are located within 0.2R200 (~0.5 Mpc) from the cluster center,
with data from the Coma Treasury Survey obtained with the Hubble Space
Telescope. The fraction of close galaxy pairs in the sample is the proxy
employed for the estimation of the merger activity. We identify 5 pairs and 1
triplet, enclosing a total of 13 galaxies, based on limits on projected
separation and line-of-sight velocity difference. Of these systems, none show
signs of ongoing interaction, and therefore we do not find any true mergers in
our sample. This negative result sets a 1{\sigma} upper limit of 1.5% per Gyr
for the major dry merger rate, consistent with the low rates expected in
present-day clusters. Detailed examination of the images of all the RS galaxies
in the sample reveals only one with low surface brightness features
identifiable as the remnant of a past merger or interaction, implying a
post-merger fraction below 2%.
