  It is common knowledge that atoms can form molecules if they attract each
other. Here, we show that it is possible to create molecules where bound states
of the atoms are not the result of attractive interactions but have the
topological origin. That is, the bound states of the atoms correspond to the
topologically protected edge states of a topological model. Such topological
molecules can be realized if the interaction strength between ultra-cold atoms
is properly modulated in time. A similar mechanism allows one to realize
topologically protected localization of an electron on a classical orbit if a
Rydberg atom is perturbed by a properly modulated microwave field.
