Can a Gemini woman get an Aries man back after a break up by acting like she don't care about what happened and they are just friends?

It depends on what happened. An astrological relationship chart and reading can be used to interpret whether or not both of you are compatible and should be with each other. But if I am just basing my answer on your Sun signs he may not be interested if he has lost his patience and has decided not to fight for the relationship.