Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
You statement in the last paragraph can be found in McDuff and Salamon's Introduction to Symplectic Topology, it's Theorem 3.4.10 in the 3rd edition (the result is only stated for compact submanifolds, but compactness isn't really used anywhere in the proof).
@IanAgol very interesting... although I suppose that since $S^1$ has noncontinuous group automorphisms it is not possible to get the topology of $\mathrm{Hom}(A, G)$ just from the group structure.
