A primary requiremnt for our fibration surface is that its boundary is exactly the
We construct our complete fibration surface by taking the union of subsurfaces, corresponding to the portion of the fibre inside and outside of the torus. We consider the boundaries of these subsurfaces, which will be blue and orange curves embedded in our torus.
Since our complete fibration is the union of the subsurfaces, wherever
outside boundary curves coincide is actually not a boundary to our complete fibration. Therefore, we can 'cancel' these portions of the boundary curves. We call these
If we consider the only the boundaries of the
outside surfaces without the