Involve: A Journal of Mathematics

• Involve
• Volume 6, Number 3 (2013), 345-368.

Extensions of the Euler–Satake characteristic for nonorientable $3$-orbifolds and indistinguishable examples

Abstract

We compute the $Fℓ$-Euler–Satake characteristics of an arbitrary closed, effective $3$-dimensional orbifold $Q$ where $Fℓ$ is a free group with $ℓ$ generators. We focus on the case of nonorientable orbifolds, extending previous results for the case of orientable orbifolds. Using these computations, we determine examples of distinct $3$-orbifolds $Q$ and $Q′$ such that $χΓES(Q)=χΓES(Q′)$ for every finitely generated discrete group $Γ$.

Article information

Source
Involve, Volume 6, Number 3 (2013), 345-368.

Dates
Accepted: 10 October 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513733592

Digital Object Identifier
doi:10.2140/involve.2013.6.345

Mathematical Reviews number (MathSciNet)
MR3101766

Zentralblatt MATH identifier
1286.57025

Citation

Carroll, Ryan; Seaton, Christopher. Extensions of the Euler–Satake characteristic for nonorientable $3$-orbifolds and indistinguishable examples. Involve 6 (2013), no. 3, 345--368. doi:10.2140/involve.2013.6.345. https://projecteuclid.org/euclid.involve/1513733592

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