The Euler characteristic of a triangulated manifold in terms of even-dimensional faces

TL;DR

This paper presents a universal formula for calculating the Euler characteristic of even-dimensional triangulated manifolds using only the counts of their even-dimensional faces, simplifying topological computations.

Contribution

It introduces a universal formula relating the Euler characteristic to even-dimensional face counts, independent of the manifold's dimension.

Findings

Derived a formula expressing Euler characteristic via even-dimensional faces

Coefficients in the formula are universal and dimension-independent

Simplifies calculations of topological invariants for triangulated manifolds

Abstract

We give a formula for the Euler characteristic of a triangulated manifold of even dimension in terms of the numbers of even-dimensional faces only. The coefficients in this formula are universal (they do not depend on the dimension of the manifold).