ABSTRACT
Architecture would seem to have an undeniable relationship to topology. A discipline of unceasing formal invention, increasingly aided by computational tools, architectural production seems to have topology fully embedded in design. Topology is curiously hard to define&. It started as a kind of geometry but it has reached into many other mathematical fields. There is a Neoplatonic component to the topological relationships that this work investigates: by assigning material behaviors, proclivities, and tendencies to the diagram, the investigation progresses according to the inconsistencies that matter itself introduces into the equation. Topology is a philosophy of relationships, and of how those relationships become established. Architecture today is a science constantly hybridized with other disciplines—not only the material sciences, but philosophy, social sciences, economics, political science, sociology. Topology is useful as a tool to map previously invisible relationships across these disciplinary boundaries. Topology can be recognized as a science and series of techniques for exploring possible relations and how they work abstractly.
