This extended abstract reports on initial investigation into a software architecture for component systems. Described is a geometrically-based, cellular framework for the organization of component computation and communication. These structures are called Cellular Component Manifolds. The starting point for this work is the observation that the concept of address space is a pervasive abstraction across all computing and communicating systems. Accordingly, a generalized model of an idealized address space is proposed. A particular geometry with a suitable algebraic structure is chosen to provide addressing within this model. This results in an n-dimensional, hierarchical, cellular-aggregate address space that is also a vector space with "nice" properties. The address space, when populated with suitable components, becomes a Cellular Component Manifold. A component system architecture is given. This software architecture consists of three major layers: component framework framework, component frameworks, and components. In addition to providing a basis for component system organization this structure natively supports a range of scientific and engineering applications. As an example, the architecture is applied to the problem of handoff management in wireless overlay networks.