Armed officers joined those from the counter terrorism command when the arrests were made at about 4am.
Police say the operation was not linked to the Olympics.
A 38-year-old woman was also arrested for alleged fraud offences and two other men were held over alleged immigration offences.
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A man, reportedly armed with a knife and a baseball bat, was detained close to the event and police cleared the area as a precaution.
A remarkably mild night
Thousands of people have gathered in the centre of Manchester for a vigil in the wake of the terror attack.