Lie's 3rd theorem

Question

Lie's 3rd theorem says that

For any Lie algebra ${\frak g}$, there exists a connected and simply connected group $G$ which algebra is (isomorphic to) ${\frak g}$

My problem is that I don't understand what does 'connected and simply connected' stand for? Since Lie groups have a manifold structure, does 'simply connected' refer to the idea of Jordan curves (closed curves that are homotopic to an inside point)?

Answer 1

Yes. If a topological space is connected, we say that it is simply connected if every closed path is homotopic to a constant path.