We compute the -Euler–Satake characteristics of an arbitrary closed, effective -dimensional orbifold where is a free group with 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 -orbifolds and such that for every finitely generated discrete group .
"Extensions of the Euler–Satake characteristic for nonorientable $3$-orbifolds and indistinguishable examples." Involve 6 (3) 345 - 368, 2013. https://doi.org/10.2140/involve.2013.6.345