The boundary operator
No. 128, 1973
(Algebraic topology)
India ink and pencil on paper, 30.5x42.5 cm.
In this zero-gravity arena, blocks remain suspended, though aligned. Their feeling of great heaviness, of powerful mass, is counterbalanced by their weightlessness and by the light and energy that they reflect, bouncing back into the abyss. Three-dimensional bodies, homeomorphic to parallelepipeds, have a boundary consisting of six rectangular faces. By gluing them together we diminish their total boundary, annihilating two rectangles each time we glue bodies together. Each gluing creates a three-dimensional body whose boundary is homeomorphic to a two- dimensional sphere. This picture illustrates the difference between the concepts of geometric and algebraic boundaries. If several polyhedra come together to form another single polyhedron, then we can compute their boundaries and form an algebraic sum, which can be used to compute the boundary of the single, larger polyhedron.
