Topological Sways That Bear Freedom Of Motion

Let us here first consider a theoretical substringular particle, that moved in the relative holomorphic direction in only one spatial dimension, over time.  The particle that is moving such, will then be of either zero spatial parameters of dimensionality or of one spatial parameter of dimensionality. Its motion would the, in this theoretical case, of a Fourier-based kinematic displacement, that would form a flat Lagrangian path as a Wilson Line -- that is being delineated as a propagating Hamiltonian index, over a sequential series of instantons.  Let us next theoretically consider an either zero-dimensional , or a one-dimensional or a two-dimensional particle that is moving homomorphically as a line that curves as is the piecewise continuous intrinsic curvature of space at each so-eluded-to individually taken point -- in a plane that is of only two spatial parameters of dimensionality, plus time.  Its motion will then tend to work to bear a topological sway, that will here have its bearings in the alterior spatial dimension that is normal to the intrinsic dimensional parameter that it is moving through.  Next, let us theoretically consider an particle that has a dimensional set of parameters that work to include up to three spatial dimensions plus time.  It is moving relatively flush in the relative holomorphic direction.  Its topological sway will then tend to bear a binary Laplacian-based coniaxial of motion -- as the said particle is moving as is the intrinsic curvature of space at each individually taken piecewise continuous iteration of instanton, in which the particle moves into the Lagrangian path of its given arbitrary Hamiltonian operand, over time.  Take this pattern.  If one had a particle that traveled in a 32 dimensional volumed space over time -- but flush in the relative holomorphic direction -- then, its topological sway may work to include a 31 dimensional coniaxial that is normal to the so-stated Lagrangian-based path of the said holomorphic-based motion of the particle here that is moving in 32 spatial dimensions plus time.  Two of the said coniaxials of this topological-based sway of this latter case will be of a Real Reimmanian-based nature, and, the other 29 coniaxials of this topological-based sway of this latter case will be of a Njenhuis-based nature.  To Be Continued!  Sam Roach.