Talk:Borel Conjecture for the 2-torus (Ex)
From Manifold Atlas
The selfhomotopy equivalences of an Eilenberg-Mac Lane space of type generally have , detected by the action of fundamental groups, and , with all other homotopy groups vanishing. In particular, is detected by the action on and all we have to do is produce a homeomorphism that acts by a given matrix . But via the identification the action of on produces such an element.
The same argument shows that the inclusion splits on In arbitrary dimensions.