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CLASSIFYING CLOSED 2-ORBIFOLDS WITH EULER CHARACTERISTICS

Published online by Cambridge University Press:  25 August 2010

WHITNEY DUVAL ,
JOHN SCHULTE ,
CHRISTOPHER SEATON  and
BRADFORD TAYLOR
WHITNEY DUVAL
Affiliation:
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
JOHN SCHULTE
Affiliation:
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
CHRISTOPHER SEATON
Affiliation:
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
BRADFORD TAYLOR
Affiliation:
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
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Abstract

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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.

Keywords

Primary 57R2057S17Secondary 22A2257P99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 555 - 574
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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