# Characteristic classes in general relativity on a modified Poincare curvature bundle

## TL;DR

This paper explores characteristic classes in general relativity, demonstrating that the Einstein--Hilbert action in four dimensions can be viewed as a second Chern-class on a modified Poincare bundle, linking cosmological constants and energy-momentum traces to topological invariants.

## Contribution

It introduces a novel perspective by relating the Einstein--Hilbert action to characteristic classes on a modified Poincare bundle, revealing new topological insights in four-dimensional gravity.

## Key findings

- Einstein--Hilbert action is equivalent to a second Chern-class in 4D.
- Cosmological constant and energy-momentum trace are divisible modulo R/Z.
- Characteristic classes are discussed for both even and odd-dimensional spacetimes.

## Abstract

Characteristic classes in space-time manifolds are discussed for both even- and odd-dimensional spacetimes. In particular, it is shown that the Einstein--Hilbert action is equivalent to a second Chern-class on a modified Poincare bundle in four dimensions. Consequently, the cosmological constant and the trace of an energy-momentum tensor become divisible modulo R/Z.