We will begin by reviewing the Morse theory of the torus T2 = S1 x S1, using the height function as our perfect Morse function (see figure below). We will see that this function is also an equivariantly perfect Morse function, with respect to a Z2 x Z2 action. One reason that this is true is that we may view T2 = S1 x S1 as the real points RP1 x RP1 of the complex variety CP1 x CP1. We will describe some results relating the (equivariant) topology of a symplectic manifold to the (equivariant) topology of its real points. In particular, in the case of T2, we will show how to answer a question arising in string theory.