  High-density cusps of compact remnants are expected to form around
supermassive black holes (SMBHs) in galactic nuclei via dynamical friction and
two-body relaxation. Due to the high density, binaries in orbit around the SMBH
can frequently undergo close encounters with compact remnants from the cusp.
This can affect the gravitational wave merger rate of compact binaries in
galactic nuclei. We investigated this process by means of high accuracy
few-body simulations, performed with a novel Monte Carlo approach. We find
that, around a SgrA*-like SMBH, three-body encounters increase the number of
mergers by a factor of 3. This occurs because close encounters can reorient
binaries with respect to their orbital plane around the SMBH, increasing the
number of Kozai-Lidov induced mergers. We obtain a binary black hole merger
rate of 1.6x10^-6/yr per Milky Way-like nucleus.
