Twisted cohomologies of wrap groups over quaternions and octonions

TL;DR

This paper explores the cohomological properties and structures of wrap groups over real, complex, quaternion, and octonion fields, including the construction of sheaves and the study of twisted cohomologies.

Contribution

It introduces the analysis of wrap groups over quaternions and octonions, including their cohomologies and sheaf structures, extending previous work over real and complex fields.

Findings

Cohomologies of wrap groups over quaternions and octonions are characterized.

Sheaves of wrap groups are constructed and analyzed.

Twisted cohomologies over quaternion and octonion fields are developed.

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.