A Generalization of Thorpe's Inequality

TL;DR

This paper generalizes Thorpe's topological inequality relating the Euler characteristic and Pontryagin number for 4k-manifolds, correcting and completing previous arguments to enhance understanding of manifold invariants.

Contribution

It introduces a broader inequality for 4k-manifolds and rectifies earlier inaccuracies in Thorpe's original work.

Findings

Established a generalized inequality for 4k-manifolds

Corrected and completed Thorpe's original arguments

Enhanced understanding of topological invariants in high-dimensional manifolds

Abstract

We present a generalization of the topological inequality of Thorpe between the Euler characteristic and $k^{th}$-Pontryagin number of a $4k$-manifold. We also correct and complete some of the arguments from the work of Thorpe in which this inequality originally appeared.