# The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds

## TL;DR

This paper extends the higher-dimensional Chern-Gauss-Bonnet formula to conformally flat manifolds with isolated singularities, broadening the understanding of geometric invariants in singular settings.

## Contribution

It generalizes the Chern-Gauss-Bonnet formula to all even dimensions for conformally flat manifolds with singularities, beyond previous four-dimensional results.

## Key findings

- Derived a higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds.
- Extended the formula to all even dimensions ≥ 4 with isolated singularities.
- Provided new insights into geometric invariants in singular geometric structures.

## Abstract

In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points, in particular obtaining the first such formula in a dimension higher than two which allows the underlying manifold to have isolated conical singularities. In the present article, we extend this result to all even dimensions $n\geq 4$ in the case of a class of conformally flat manifolds.