Generalization of Higher Order Homomorphism in Configuration Complexes

Abstract

In this research, Grassmannian complex (Configuration Complex) is being introduced in a generalized form. Its 4th and 5th order complexes are being constructed at first, then Nth order generalization is being discussed. For this purpose, higher order mixed partial differential morphisms between free abelian group generated by projective configuration of points will used. Furthermore, in this work, the associated diagrams of these complexes are shown to be commutative.