Structural Geometric Topology by Albert P. Carpenter

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Structural Geometric Topology is one of four mathematical disciplines that result from the systematic unification of geometry and topology. The others are: Structural Metageometry, Structural Topological Geometry and Structural Metatopology. The unifying theory common to each is structuralism as found in theoretical chemistry and theoretical biology. So conceived, the relationship between each compound discipline is of components to structures. In Structural Geometric Topology for example, polyhedra, polygons, lines and points each function as components for topological structures such as knots, links, tori/handlebodies, Mobius strips, braids, weaves and Kleinian structures etc.

These objects are the product of a new methodology for cognitive mathematics born of Cognitive Science. In the latter field, it is known as conceptual integration, but I have systematized it using qualitative matrices and named the process “Systematic Conceptual Integration” (see Table below).

The use of color is intended to elucidate the substructures of which the objects are built.

For every object there would ideally be an accompanying mathematical data sheet with its name, classification and properties etc. Unfortunately, that is beyond my abilities  at this time. However, included at this site is a sample data sheet that would be filled out for each object in the creation of a database. In addition to the mathematical data sheet, some day in the future there will also be a physical data sheet for each object depicting its physical analog.

As for the pointal models, there already exists an extensive study of these objects at: the Please go there to see them.

Also see my work at:

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