Relationship postdoc-supervisor I would like to ask you some clarifications about the relationship between postdoctoral fellow and supervisor. In particular, does the postdoctoral fellow need to work only on the supervisor's research or there is some room for its own research? 

Thanks!
This is very field specific, and possibly country specific as well.

In math in the US, most postdocs are hired by the department and it's generally considered a positive if they're also working on their own independent research as well as work with their supervisor.