The question of what is a perceptual object is one of the most central and also controversial issues in cognitive science. According to the topological approach to perceptual organization, the core intuitive notion of an object-the holistic identity preserved over shapechanging transformations-may be characterized precisely as topological invariance. Here we show that, across a series of multipleobject tracking tasks, performance was not disrupted when the moving items underwent massive featural changes. However, performance was significantly impaired when the items changed their topological properties of holes, demonstrating that topological invariance constrains what counts as an object in the first place. Consistent with previous findings, fMRI studies indicated that the anterior temporal lobe may be involved in the formation of object representation defined by topological constraints.W hat is a perceptual object? This question has become one of the most central and also controversial issues in many areas of the cognitive sciences (1-13). After decades of research, we still do not yet know exactly what counts as an object in the first place. In natural language and in everyday life, objects can be almost anything (e.g., from a drop of water, to a bird, to a car). It is a major challenge to define precisely, beyond commonsense labeling, what constitutes an object, or, in other words, how we abstract from every variety of objects the basic constraint on objecthood applied to all objects by definition.We propose that the core intuitive notion of an object is its holistic identity preserved over shape-changing transformations (14). This identity can be characterized precisely as topological invariance † , and the extraction of topological properties serves as the starting point for the formation of an object representation (14). Consider a flying bird. The actual shape of the bird always is subject to change because of its motion (which may be nonrigid) or because of changes of illumination. Nonetheless, the phenomenal impression will be that, regardless of the changes in its featural properties (e.g., location, orientation, size, and shape), the bird retains its identity as a single connected entity (an object) over such deformations. Here the invariant of connectivity is precisely one of the topological properties. (Topology sometimes is referred to as "rubber-sheet geometry." The topological transformation can be imagined as rubber-sheet deformations such as bending, twisting, stretching, and shrinking but disallowing tearing apart or gluing together parts. The main topics of interest in topology are the properties that remain unchanged by such continuous deformations. In this kind of rubber-sheet distortion, the number of holes remains invariant and hence is a topological property.)A key but counterintuitive prediction of this topological account of perceptual objects is that the topological change of a figure (e.g., the sudden appearance of a hole in a solid figure) should disturb its object continuity. A to...