# The Real Graded Brauer group

## TL;DR

This paper introduces a Real version of the Brauer--Wall group for vector bundles, compares it to the topological Witt group, and explores their topological aspects over real varieties.

## Contribution

It defines a Real Brauer--Wall group and relates it to the topological Witt group, providing new insights into their topological invariants over real varieties.

## Key findings

- The Real Brauer--Wall group is introduced and characterized.
- Comparison with the topological Witt group reveals their relationship.
- The invariants capture topological parts of these algebraic structures.

## Abstract

We introduce a version of the Brauer--Wall group for Real vector bundles of algebras (in the sense of Atiyah), and compare it to the topological analogue of the Witt group. For varieties over the reals, these invariants capture the topological parts of the Brauer--Wall and Witt groups.