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

Ryan Carroll and Christopher Seaton

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We compute the F-Euler–Satake characteristics of an arbitrary closed, effective 3-dimensional orbifold Q where F 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 3-orbifolds Q and Q such that χΓES(Q)=χΓES(Q) for every finitely generated discrete group Γ.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R18: Topology and geometry of orbifolds 57R20: Characteristic classes and numbers
Secondary: 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 57S17: Finite transformation groups

orbifold $3$-orbifold Euler–Satake characteristic orbifold Euler characteristic


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.

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