Twisted cohomologies of wrap groups over quaternions and octonions

Abstract

This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups and their structure are investigated. Sheaves of wrap groups are constructed and studied. Moreover, twisted cohomologies and sheaves over quaternions and octonions are investigated as well.