135054.fig.001a
(a)   A loop can be contracted to a point without leaving the sphere surface
135054.fig.001b
(b) Gradual Construction of a torus based on a rectangle
135054.fig.001c
(c) Any chromatic loops cannot be contracted to a point without leaving the torus surface
135054.fig.001d
(d) Hemispheres mapped to a Whole Sphere
Figure 1: Diagram of manifold.