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We present a non-contact manipulation method for micron scale objects using locally induced rotational fluid flows created by groups of untethered magnetic micro-manipulators. The magnetic micro-manipulators are rotated in a viscous fluid by an externally generated magnetic field to create rotational flows, which act to move micro-objects in the flow region. One single spherical micro-manipulator is used to manipulate one object at a time, while an array of micro-manipulators spin in synchrony on a surface patterned with magnetic micro-docks to create reconfigurable fluidic channels for simultaneous transportation of multiple objects. The induced rotational flow field and the resulting hydrodynamic forces on the micro-objects are studied using both finite element solutions and analytical models from previous studies. These results are compared with experiment to determine manipulation characteristics for the complex flows. Due to its untethered and non-contact operation, this micro-manipulation method could be used to quickly move fragile or non-fragile micro-objects in inaccessible or enclosed spaces such as in lab-on-a-chip devices.