Session 9 of Course 11 About Orbifolds

Orbifolds may exist in many shapes.  Idealy, orbifolds exist in a rounded shape.  A round orbifold is not necessary spherical, though.  Orbifolds, including round-like shaped orbifolds, are generally not spherical -- actually.  A round orbifold that is not spherical as a Ward-Caucy basis has permutations.  These permutations are indications of space that exists along the outer topology of the orbifold.  These permutations may be relatively small, or, in other cases, these permutations may be relatively large -- or somewhere in-between.  What one would consider as a small, medium-sized, or large permutation in an orbifold is, to a certain extent, subjective to the physicist of whom would be working to determine the general Laplacian-based mapping of the topology of a given arbitrary orbifold.  An individual orbifold may have permutations of many sizes and shapes.  An orbifold may have some relatively small permutations, some relatively medium sized permutations, and also some relatively large-sized permutations -- when relating to the general Hodge-Index basis of the mentioned orbifold.  An orbifold may occasionally have just some relatively large and some relatively medium-sized permutations, yet, not having any relatively small-sized permutations -- when relating to the general Hodge-Index basis of the mentioned orbifold.  An orbifold may have some relatively large-sized permutations and some relatively small-sized permutations, yet, not having any medium-sized permutations -- when relating to the general Hodge-Index basis of the mentioned orbifold.  An orbifold may have some relatively medium-sized permutations and some relatively small-sized permutations, yet without having what one may consider to be any large-sized permutations -- when relating to the general Hodge-Index basis of the mentioned orbifold.  One may consider certain orbifolds to have only moderately sized permutations, when in light of the general Hodge-Volume of the said orbifold.  One may consider certain orbifolds to have only large-sized permutaions, when in light of the general Hodge-Volume of the said orbifold.  Or, one may consider certain orbifolds to have only small-sized permutations, when in light of the general Hodge-Volume of the said orbifold.  When I am about to write, "have only", I am reffering to a certain format of a given arbitrary case-type scenario.  Some orbifolds may only have permutations at the relative norm-to-holomorphic Laplacian-based positioning of the topology of the said orbifold.  Some orbifolds may have only permutaitons at the relative holomorphic Laplacian-based positioning of the topology of the said orbifold.  Some orbifolds may have only permutaions at the relative norm-to-reverse-holomorphic Laplacian-based positioning of the topology of the said orbifold.  Some orbifolds may have only permutations at the relative reverse-holomorphic Laplacian-based positioning of the topology of the said orbifold.  Some orbifolds may have only permutations at the relative norm-to-holomorphic and the reverse-norm-to-holomorphic Laplacian-based positioning of the topology of the said orbifold.  Some orbifolds may have only permutations along the holomorphic and the reverse holomorphic Laplacian-based positioning of the topology of the said orbifold.  An orbifold may have only permutations at the norm-to-holomorphic and the holomorphic Laplacian-based positioning of the topology of the said orbifold.  An orbifold may have only permutaitons at the norm-to-reverse-holomorphic and the holomorphic Laplacian-based positioning of the topology of the said orbifold.  An orbifold may have only permutations at the norm-to-reverse-holomorphic and the reverse-holomorphic Laplacian-based positioning of the topology of the said orbifold.  Any combination as such may exist in their own given arbitray cases.  One may subjectively consider orbifolds to have any combination of relatively large, medium-sized, and/or small-sized permutations, when one considers the relative Hodge-based Index of the coreleative orbifolds. at any combination of relative positioning as to where the said given arbitrary permutations are at in certain case scenarios.  I will continue with the suspense later!  Sincerely, Sam Roach.