On the Euler Characteristic of Odd-Dimensional Orbifolds and Their Boundaries

TL;DR

This paper proves a relationship between the Euler characteristic of a compact odd-dimensional orbifold and its boundary, showing it is half of the boundary's Euler characteristic.

Contribution

It establishes a new theoretical result linking the Euler characteristic of odd-dimensional orbifolds to their boundaries.

Findings

Euler characteristic of odd-dimensional orbifolds is half that of their boundary

Provides a mathematical proof for the relationship

Advances understanding of orbifold topology

Abstract

In this work we prove that for a compact odd-dimensional orbifold its Euler characteristic is half of the Euler characteristic of its boundary.