On the universal and generalized orbifold Euler characteristics

TL;DR

This paper explores the universal orbifold Euler characteristic and its generalizations for various finitely generated groups, demonstrating how specific group-based invariants determine the universal characteristic.

Contribution

It introduces the concept of $A$-Euler characteristics for finitely generated groups and shows their role in determining the universal orbifold Euler characteristic.

Findings

$A$-Euler characteristics for groups of the form $A' imes Z$ determine the universal orbifold Euler characteristic.

The paper establishes a relationship between group invariants and orbifold topological invariants.

It provides a framework for understanding orbifold invariants through finitely generated groups.

Abstract

We discuss the universal orbifold Euler characteristic and generalized orbifold Euler characteristics corresponding to finitely generated groups $A$ (the $A$-Euler characteristics). We show that the collection of all $A$-Euler characteristics for $A$ of the form $A'\times Z$ ($Z$ is the group of integers) with finite $A'$ determine the universal orbifold Euler characteristic.