Preprint Article Version 1 This version is not peer-reviewed

Generalization of the Geometry of Cathelineau Infinitesimal and Grassmannian Chain Complexes

Version 1 : Received: 14 March 2017 / Approved: 15 March 2017 / Online: 15 March 2017 (08:04:30 CET)

How to cite: Khalid, M.; Iqbal, A.; Khan, J. Generalization of the Geometry of Cathelineau Infinitesimal and Grassmannian Chain Complexes. Preprints 2017, 2017030098 (doi: 10.20944/preprints201703.0098.v1). Khalid, M.; Iqbal, A.; Khan, J. Generalization of the Geometry of Cathelineau Infinitesimal and Grassmannian Chain Complexes. Preprints 2017, 2017030098 (doi: 10.20944/preprints201703.0098.v1).

Abstract

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

Subject Areas

homomorphism; Grassmannian; generalized geometry; cathelineau's complex