A Little As To The Mathematics Of Cohomology

When one is to work to derive those mathematical expressions -- that are here to be utilized in so as to help at describing cohomological eigenindices and cohomological eigenstates, -- one is to initially work to derive what I term of here as being the respective given arbitrary genus of a "knotting" equation.  Such a said "knotting" equation is here to be contingent upon a Real Reimman manifold, of which is named here as "W."  If one is to try to derive a correlative Complex manifold G(c), one may take one or more Li-operators to be applied upon the said W manifold, in order to get the said G(c) manifold -- in the process of working to determine such a general condition.  In the process of working to derive such so-inferred knotting equations, one is here to be working to translate one given arbitrary Minkowski Space into a correlative given arbitrary Hilbert Space.  I can think of six general genre of knotting equations from the "top of my head."  These would be:  One for an f-field, one for a d-field, one for a p-field, one for a graviton field, one for a gravitino field, and one for a neutrino field.  This may be enough for you to digest for now.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Hamiltonian Operations Of Gravity

Often, superstrings of a Hamiltonian operation of gravity, may simultaneously (via the vantage-point of a central conipoint), act as both a graviton and a gravitino.  This is when a Ward-Cauchy-based particle of a Hamiltonian operation of gravity, is to bear both radial and transversal characteristics, over the course of the same distinct iterations of group-related instanton.  So, let's say that, over the course of one specific iteration of instanton, that a Ward-Cauchy-based gravitational particle is to be at both one positioning of a fractal of angular momentum and at one position of a fractal of spin-orbital momentum.  Next, at the ensuing iteration of instanton, the just mentioned particle is to be distributed in such a delineation -- to where its fractal tense of angular momentum had to have just altered by one Planck Length, while its fractal tense of spin-orbital momentum had to have just altered by one Planck Radii.  Let us next say that the just mentioned tendency, is then to re-occur for a significant number of iterations of group-related instanton.  A graviton is a superstring of a Hamiltonian operation of gravity, that works to involve the transversal motion of the so-eluded-to eigenstate -- whereas, a gravitino is a superstring of a Hamiltonian operation of gravity, that works to involve the radial motion of the so-eluded-to eigenstate.  One could then say, when such a just mentioned gravitational particle is to display both a transversal and a radial motion -- over the same general tendency of motion -- that it is to act as both a graviton and as a gravitino simultaneously (via the vantage-point of a central conipoint).  One could then say, that such a particle may be considered as a unitary dual-state of gravitational eigenstate, that is to exhibit the gauged activity of both a fractal tense of angular momentum and the gauged activity of a fractal tense of spin-orbital momentum -- over the course of the same evenly gauged Hamiltonian operation.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little Explanation As To the Morphologies

What I mean by the condition that Neilson-Kollosh ghosts bear a "hyperbolically toroidal" shape or morphology, is that the toroidal-based nature of the ghost anomalies that work to comprise any given arbitrary Neilson-Kolosh cohomological-based set of indices, tends to slope either hyperbolically inward -- in a converging genus of mappable tracing -- or, these often may slope hyperbollically outward -- in a diverging genus of mappable tracing, as such a format or genus of a set of cohomological-based indices, that work to comprise any respective given arbitrary Neilson-Kollosh ghost anomaly, that may be traced in a mappable manner, through any given arbitrary Lagrangian-based path -- that the directly corresponding graviton or gravitino, that such a case scenario eludes to -- as such a respective given arbitrary graviton or gravitino is being propagated through, over time.  So, if one is dealing specifically with the Lagrangian-based path of a graviton -- the respective directly corresponding ghost anomaly that works to form the correlative set of cohomological-based indices -- will be formed in so as to make a mappable tracing of simply a given arbitrary toroidal-based configuration, that is either hyperbolically converging or hyperbollically diverging, that is homotopically Hilbert or volume-spaced, with an annulus --  throughout that region in whih such a ghost anomaly is formed, by the physical memory of the mappable tracing of the projection of the trajectory of the directly corresponding graviton, of this given arbitrary case scenario.  Yet, if one is, instead, dealing with the Lagrangian-based path of a gravitino, the respective directly corresponding ghost anomaly that works to form the correlative set of cohomological-based indices -- will be formed, in so as to make a mappable tracing, that may be extrapolated as being the shape of the perimeter of a given arbitrary toroidal-based annulus of a configuration that is either hyperbolically Minkowski or flat-spaced, in either a relatively holomorphic-based converging manner or in a relatively holomorphic-based diverging manner -- throughout that region in which such a ghost anomaly is formed, by the physical memory of the mappable tracing of the projection of the trajectory of the directly corresponding gravitino of this given arbitrary case scenario.  The reason being -- that, any given arbitrary graviton works to bear more of a transversal-based angular Hamiltonian-based fractal of momentum in the substringular, whereas, any given arbitrary gravitino works to bear more of a radial-based Hamiltonian-based fractal of momentum in the substringular.  To Be Continued!  Sam.