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Abstract
We compute the
F ℓ -Euler–Satake
characteristics of an arbitrary closed, effective
3 -dimensional
orbifold
Q where
F ℓ 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
χ Γ ES ( Q )
= χ Γ ES ( Q ′ ) for every finitely
generated discrete group
Γ .
Keywords
orbifold, $3$-orbifold, Euler–Satake characteristic,
orbifold Euler characteristic
Mathematical Subject Classification 2010
Primary: 57R18, 57R20
Secondary: 22A22, 57S17
Milestones
Received: 10 August 2012
Accepted: 10 October 2012
Published: 8 September 2013
Communicated by Colin Adams