# Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulators

## TL;DR

This paper develops a geometric approach to topological invariants in time-reversal-symmetric topological insulators using square roots of gerbe holonomies, linking mathematical structures to physical properties.

## Contribution

It introduces a novel construction of a square root of gerbe holonomy and applies it to define topological invariants for symmetric insulators.

## Key findings

- Constructed a distinguished square root of gerbe holonomy
- Linked gerbe holonomy to topological invariants in insulators
- Applied the framework to static and periodically driven systems

## Abstract

The Feynman amplitudes with the two-dimensional Wess-Zumino action functional have a geometric interpretation as bundle gerbe holonomy. We present details of the construction of a distinguished square root of such holonomy and of a related 3d-index and briefly recall the application of those to the building of topological invariants for time-reversal-symmetric two- and three-dimensional crystals, both static and periodically forced.