Symmetries Of Cohomologies

Let us consider a given arbitrary quantum of discrete energy permittivity, during BRST.  This is when both the Polyakov Action and the Beti Action are happening to the correlative discrete quantum of energy, simultaneously -- through the vantage-point of a central conipoint.  The so-eluded-to superstring and its counterstring, during such a tense of a gauge-metric, are not to then to be in the process of going through a Lagrangian-related genus of motion -- since this is here to be happening, over the course of one discrete instant of time.  As this is happening, -- the said superstring is to be vibrating at the correlative proximal locus of its Sterling Approximation.  During BRST, the said string -- whether the correlative superstring of discrete energy permittivity is here to be either of a bosonic nature or whether it is here to be of a fermionic nature -- is here to form a vibrational oscillation, that is to be either of a respective harmonic nature or of a respective anharmonic nature.  (Such a said vibration is here to be of a harmonic oscillation if it is of a bosonic nature, or such a said vibration is here to be of an anharmonic oscillation if it is of an fermionic nature.)  As an aside:  The topology itself of a superstring at the Poincare level, that is inherent to a discrete quantum of energy permittivity, is extraordinarily smaller in thickness than the respective circumference or its respective length than such a so-eluded-to superstring.  (As a general idea so that you get the jist -- a superstring is on the order of 10^(-43)* as thin, as it is respectively round (bosonic) or long (fermionic.)   So, as such a said given arbitrary superstring of discrete energy permittivity and its directly corresponding counterstring, are vibrating during BRST -- the directly corresponding topology of the holonomic substrate of the said discrete quantum of energy -- is to be interacting in a Gliosis manner with the norm-state-projections that surround it, in so as to work to form what may here to termed of here as a Gliosis-Sherk-Olive cohomology.  Such a GSO cohomology, tends to be of a toroidal-related shape for such a so-eluded-to bosonic string, and such a GSO cohomology tends to be either disc-shaped, washer-shaped ( if the correlative superstring is swivel-shaped), or conical-shaped, for such a so-eluded-to fermionic string.  Consequently, the GSO cohomology of a superstring of discrete energy permittivity, that is bosonic in nature -- tends to be symmetric in differential geometry to its directly corresponding counterstring, during BRST, -- whereas, the GSO cohomology of a superstring of discrete energy permittivity, that is fermionic in nature -- tends to be assymetric in differential geometry to its directly corresponding counterstring, during BRST.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.