Notes on obstructions in the hyperbolic Clifford algebra bundle structure

TL;DR

This paper analyzes obstructions in the hyperbolic Clifford algebra bundle, showing that unlike classical cases, hyperbolic frame bundles can always be lifted, enabling consistent spinor structures.

Contribution

It demonstrates that hyperbolic Clifford bundles lack topological obstructions for lifting, allowing universal definition of spinor structures, unlike classical tangent bundles.

Findings

Hyperbolic frame bundle admits lifting without topological obstructions.

Spinor structures can always be defined in hyperbolic Clifford bundles.

Obstructions differ from classical tangent bundle cases.

Abstract

Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney sum, it is shown that, unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles.