There is a topology of objects. In mathematics topology is sometimes referred to as “rubber sheet geometry”. What is studied here is not the fixed metric properties of a shape– such as the degrees of each angle of a triangle –but rather the permutations a shape can undergo through operations of bending, stretching, twisting, and folding. For example, a triangle can be turned into a square by folding over one of its vertices. In topological language, triangles and squares are thus topologically equivalent because there is a series of operations through which the one can be transformed into the other. Likewise, an equilateral triangle can be turned into an right triangle by pulling and stretching one of its vertices. Topology is a dynamic geometry that thinks shapes in terms of movements and transformations.

The claim that objects are topological is the claim that they are subject to permutations that transform both their phenotype and their qualities. As I have argued in The Democracy of Objects, every object is characterized by an endo-structure and the exo-relations it entertains to other objects. The endo-structure of an object is its internal structure, coupled with the way its potentialities or attractors are related to one another (recall that I argue that the being of an object is not defined by it’s qualities but by its potentials or capacities, by what the object can do. The qualities of an object such as its shape, its color, its density, etc, are actions on the part of objects; events that the object produces as a result of what it does.