  This article examines how the physical presence of field energy and
particulate matter can be interpreted in terms of the topological properties of
space-time. The theory is developed in terms of vector and matrix equations of
exterior differential systems, which are not constrained by tensor
diffeomorphic equivalences. The first postulate defines the field properties (a
vector space continuum) of the Cosmological Vacuum in terms of matrices of
basis functions that map exact differentials into neighborhoods of exterior
differential 1-forms (potentials). The second postulate requires that the field
equations must satisfy the First Law of Thermodynamics dynamically created in
terms of the Lie differential with respect to a process direction field acting
on the exterior differential forms that encode the thermodynamic system. The
vector space of infinitesimals need not be global and its compliment is used to
define particle properties as topological defects embedded in the field vector
space. The potentials, as exterior differential 1-forms, are not (necessarily)
uniquely integrable: the fibers can be twisted, leading to possible Chiral
matrix arrays of certain 3-forms defined as Topological Torsion and Topological
Spin. A significant result demonstrates how the coefficients of Affine Torsion
are related to the concept of Field excitations (mass and charge); another
demonstrates how thermodynamic evolution can describe the emergence of
topological defects in the physical vacuum.
