  We show that it is possible to topologically induce or quench the Kondo
resonance in the conductance of a single-molecule magnet (S>1/2) strongly
coupled to metallic leads. This can be achieved by applying a magnetic field
perpendicular to the molecule easy axis and works for both full- and
half-integer spin cases. The effect is caused by the Berry phase interference
between two quantum tunneling paths of the molecule's spin. We have calculated
the renormalized Berry phase oscillations of the Kondo peaks as a function of
the transverse magnetic field as well as the conductance of the molecule by
means of the poor man's scaling method. We propose to use a new variety of the
single-molecule magnet Ni4 for the experimental observation of this phenomenon.
