Impact of Polynomial Time Algorithm for an NP Complete problem on Complexity Theory
If P=NP, then it follows that P=co-NP, and NP=NP-complete (i.e. there are no NP-intermediate problems, which are in NP but not NP-complete).

But there are plenty of other divisions in the hierarchy which might still hold, and might not. P=NP wouldn't necessarily tell us anything about this.

On the higher end of things, how does NP relate to PSPACE? It's entirely possible that they're the same (only if P=NP: if P≠NP, they're definitely different), in which case all the classes in the middle (such as PP, which uses a probabilistic Turing machine) are collapsed together too.

On the lower end, how does P relate to L (logarithmic space)? There are various classes between these ones too, such as NL (nondeterministic log space), and these might all be collapsed into a single class also.