Non-commutativity Over Canonical Suspension η for Genus g ≥1 in Hypercomplex Structures for Potential ρϕ

Abstract

Any matrix multiplication is non-commutative which has been shown here in terms of suspension‡, annihilator, and factor as established over a ring following the parameter k over a set of elements upto n for an operator to map the ring R to its opposite Rop having been through a continuous representation of permutation upto n-cycles being satisfied for a factor f along with its inverse  f-1 over a denoted orbit γ on k-parameterized ring justified via suspension η ∈ η0, η1 implying the same global non-commutativity for the annihilator A. This will be used for the construction of the genus–alteration scenario where the suspension η0 acting with its opponent   η1 on any topological space  J can alter the geometry making a change in the manifolds for taking over the Boolean (1,0) satisfying the concerned operations.