Actually, this is wrong.
Compressor and turbine have to be linked, otherwise the engine couldn't run
What would drive the compressor to provide the combustors with "new" air and start another cycle?
N1 and N2 represent the speed of the two stages of the engine. N1 is the low pressure compressor/turbine and fan, and N2 is the high pressure compressor and turbine. N1 and N2 run independently on most engines.
If you have an N3 like on some RR engines than this is the high pressure stage, and N2 represents the RPM of the intermediate stage.
A free running turbine (= a turbine stage not linked to a compressor) is used to drive the rotor or propeller via a gearbox in turboshaft engines but is not present on normal jet engines.