Structural Geometric Topology II by Albert P. Carpenter

Home » About


This site is the second part of my first site entitled Structural Geometric Topology ( This one is a continuation of the last and is constructed with the same idea that these models are of both molecular and mathematical interest.

Structural Geometric Topology is one of four mathematical disciplines that result form 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.

Thus, Structural Geometric Topology can be defined as the study of topological objects such as Tori/Handlebodies, Annuli/Sieves, Mobius strips/Structures, Knots and Links that are composed of geometric objects such as points, lines, polygons and polyhedra. By conceiving of the discipline in this way it is possible to construct a wealth of models for study.

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”. For an outline of this method please see the Methodology page on this site.

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

I would like to acknowledge the pioneering work in Polyhedral Topology of B.M. Stewart as published in his book; Adventures Among the Toroids.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: