Homotopic Waves -- Homotopic Residue

 Homotopic waves may often help at working to describe metric(al)-related associations of dimensional-related pulsations.  So; when a given arbitrary physical entity, that is here to be exhibiting the general characteristic of acting as a topological manifold, in which it is here to be considered in lieu of its Ward-Cauchy-Based nature, is thence to change or alter in its respective physical attribute of dimensional-related pulsation, then, not only will the given arbitrary entity of topological manifold, of such a respective case, tend to work to form a metric-based Chern-Simons singularity -- at the covariant "point" in duration, at which such an inferred set of discrete energy quanta, is here to have phased into such a said change in its dimensional-related pulsation, yet, in the process of doing so, -- this general process that has just been eluded-to here, will also tend to work to involve, the eminent proximal adjutant flow, in the dispensation of its directly associated tense of energy-related indices, over a discrete increment of time. (That is, as this is taken over the course of a directly corresponding Fourier Transformation.) Such a general genus of an eminent adjutant flow, in the dispensation of a tense of energy-related indices, as taken over a Fourier Transformation, is directly associated with the general Ward-Cauchy-related concept, of what I term of as being the physical condition of "homotopic residue." To Be Continued! Sincerely, SAM ROACH. (1989).

Indistinguishably Different Cohomological Indices

Although the cohomological eigenindices, that are here to apparentenly be "stuck" to any one given arbitrary GSO on-shell-related Ward-Cauchy-based kinematic structure, may "appear" to be stationed permanently there, in so as to being here in a tense of a general genus of an abelian group --  these specific indices are here to be constantly replaced and amended, in an indistinguishably different manner over time.  These cohomological indices may here apparently be spontaneously "stuck" to the external shell of the proximal locus -- that is of the topological stratum of the here directly pertinent superstrings, yet, these specific indices, that are here to appear as being kept as being Gliosis to the topological surface of the so-eluded-to discrete energy at the Poincare level, -- are, in reality, to constantly be in a flux, in which cohomolgical eigenindices are constantly leaving and being brought into the proximal locus of the topological stratum of such said superstrings, -- in so as to work to allow for the "appearance" of there to here be Ward-Cauchy-related phenomenology, that seems from an observer to be "stuck" to this earlier mentioned proximal local region -- that is of these said superstrings of discrete energy permittivity.
This is part of as to why I have equated cohomological eigenindices to ghost anomalies -- since the specific eigenindices that work to form a cohomological structure,  are constantly being brought in and taken away, -- in a manner that is here to appear as being "indistinguishably different."  Ghost anomalies refer here, in part, in my string theory model, to the relatively transient nature of the vast array of specific homological and cohomological eigenindices.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two As To Solitons

If a Ward-Cauchy-related phenomenon, is of such a nature, to where it may be described of here as being a soliton, The following must tend to hold as being true:

1) Those eigenstates, that work to directly correspond to the cotangent bundle of said soliton -- will work to eminently involve, what may be described of here as Li-based spaces.

2)  The said phenomenon will work to describe a set of eigenstates, whose Stoke's-related indices, will be both individually taken as well as being group-taken, -- as an integrative set of holographic spaces, that are of a cotangent bundle, that will work here to be of an overall scenario, that is of a maximum of 26 spatial dimensions plus time.  (Since this is of a Minkowski or of a flat-spaced Ricci curvature, -- and flat-space is of a maximum of 26 spatial dimensions plus time.)

3)  As such a said phenomenon is to be a soliton, the absolute value of its Beti number will not vary here, -- when this is taken for those individually taken superstrings, that work to help in forming the said soliton.

&4) The Fourier-related activity of the said soliton, will work to form a given arbitrary homology-based setting -- that is of either a symplectic tense of homology (a cohomology), or, of a Legendre tense of homology (Khovanov), -- that will be mappable, as going into a certain given arbitrary tense of a holomorphic motion, that is here to be propagated, over the spacing of a flat or a Minkowski-related Hamiltonian operand, over time.

Clifford Differentiation

A tense of a Clifford differentiation, will tend to elude to the presence of the generation of cohomological indices, by a given arbitrary source, -- whereas a tense of a Dirac Clifford differentiation, will instead tend to elude to the presence of the degeneration of cohomological indices , by a given arbitrary source. I will continue with the suspense later!  To Be Continued!  Sam Roach.