Glasgow Mathematical Journal

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Glasgow Mathematical Journal (2010), 52:555-574 Cambridge University Press
Copyright © Glasgow Mathematical Journal Trust 2010
doi:10.1017/S001708951000042X

Research Article

CLASSIFYING CLOSED 2-ORBIFOLDS WITH EULER CHARACTERISTICS


WHITNEY DUVALa1, JOHN SCHULTEa1, CHRISTOPHER SEATONa1 and BRADFORD TAYLORa1

a1 Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112, USA e-mails: whitney.duval@gmail.com, johnschulte1987@gmail.com, bradfordptaylor@gmail.com; seatonc@rhodes.edu
Article author query
duval w [Google Scholar]
schulte j [Google Scholar]
seaton c [Google Scholar]
taylor b [Google Scholar]

Abstract

We determine the extent to which the collection of Γ-Euler–Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the Γ-Euler–Satake characteristics corresponding to free or free abelian Γ and are not classified by those corresponding to any finite set of finitely generated discrete groups. These results demonstrate that the Γ-Euler–Satake characteristics corresponding to free abelian Γ constitute new invariants of orbifolds. Similarly, we show that such a classification is neither possible for non-orientable 2-orbifolds nor for non-effective 2-orbifolds using any collection of groups Γ.

(Received May 15 2009)

(Revised December 21 2009)

(Accepted June 25 2010)

2010 Mathematics Subject ClassificationPrimary 57R20; 57S17; Secondary 22A22; 57P99