Vol. 6, No. 3, 2013

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

Ryan Carroll and Christopher Seaton

Vol. 6 (2013), No. 3, 345–368

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.

orbifold, $3$-orbifold, Euler–Satake characteristic, orbifold Euler characteristic
Mathematical Subject Classification 2010
Primary: 57R18, 57R20
Secondary: 22A22, 57S17
Received: 10 August 2012
Accepted: 10 October 2012
Published: 8 September 2013

Communicated by Colin Adams
Ryan Carroll
Department of Mathematics
University of California
Santa Cruz, CA 95064
United States
Christopher Seaton
Department of Mathematics and Computer Science
Rhodes College
2000 North Parkway
Memphis, TN 38112
United States