Part Four of the Thirteenth Session of Course 14

The contour of a two-dimensional world-sheet of a one-dimensional superstring of discrete energy permttivity is the cohomology of the given one-dimensional string's world-sheet.  The contour of a three-dimensional world-sheet of a two-dimensional superstring of discrete energy permittivity is the cohomology of the given two-dimensional string's world-sheet.  When the cohomology of a superstring's world-sheet is smoothly interconnected, then, the limit of this cohomology exists throughout that whole space of the core field density of the corresponding world-sheet.  Multiple world-sheets may be interconnected to form a cohomology -- whose limit exists throughout a given space.  When the cohomologies of a world-sheet is not smoothly interconneced at any given arbitrary sector that may be considered by extrapolation, then, the limit of the said cohomolgy of the world-sheet that was just eluded to, at that spot that is here to be considered, does not exist.  (There is a singularity at the locus of the just eluded to spot.)  Cohomology that is smoothly connected is considered to be a Real-based cohomology. Whereas, cohomology that is not smoothly connected is considered to be an Imaginary, or Njenhuis-based cohomology.  For cohomology to even be considered to act as a Njenhuis-based cohomology at a given arbitrary locus, there needs to be some sort of a tangency of interaction that exists in-between the world-sheets that are bound in some sort of a Gliossi manner or another in order to work to define the eigenspace of that cohomology that is to be considered here by extrapolation.