  In the framework of digital topology, we study structural and topological
properties of digital n-dimensional manifolds. We introduce the notion of
simple connectedness of a digital space and prove that if M and N are homotopy
equivalent digital spaces and M is simply connected, then so is N. We show that
a simply connected digital 2-manifold is the digital 2-sphere and a simply
connected digital 3-manifold is the digital 3-sphere. This property can be
considered as a digital form of the Poincar\'e conjecture for continuous
three-manifolds.
