Homology of the 3-torus

Question

I've been learning about Morse homology, and I find it easy to compute the homology group of surfaces embedded in R3 by defining a Morse function on it, seeking the critical points and the stable und unstable manifolds etc, but what if I am to compute the homology of manifolds of a greater dimension? for example, if a take the 3-torus (or the n-torus in general), how would I proceed to calculate Hn?

Answer 1

I believe the question is: what is a nice formula for embedding a torus in $\mathbb{R}^4.$ Once you have that, you can compute the critical points, etc. The nicest is presumably the Clifford Torus. The OP can compute the critical points of his favorite height function.