Part One of the Fifteenth Session of Course 14 About Group Action

The mapped-out path of one-dimensional superstrings -- as the traceable mapping that acts as the physical memory as to the relatively given arbitrary recent trajectory of the projection of the just mentioned delineated and redelineated one-dimensional superstrings of discrete energy permittivity -- as the directly associated ghost anomalies that act as the actual physical memory of the mentioned world-sheets, of which correspond to the extrapolated history of the kinematic differentiation of the said one-dimensional superstrings -- form a commutation that acts as an inter-relationship of the mentioned physical memory -- with its local gauge-action-based surroundings, forms a cohomological-based field of the said directly corresponding ghost anomalies.  This activity works to cause the overall actual spatial field density of the corresponding respective world-sheets to have a dimensionality that is conformally two-dimensional -- at the Poincaire level of the relatively holomorphic end of the Lagrangian eigenlocus, as to where the eluded to world-sheet may be generally extrapolated at as last iterating in -- in so as to form a relative group instanton (as an instant under consideration).  Likewise, the mapped-out path of a two-dimensional superstring of discrete energy permittivity forms a ghost anomaly-based field that is three-dimensional at a relatively considered Poincaire level of vantage-point -- at an endpoint of a Lagrangian locus that may be extrapolated at a given arbitrary iteration of a group instanton metrical vantage-point, that acts as an instant under consideration.  Such a field also forms a covariant isometric commutation with its local codifferetiable, codeterminable surroundings.