Tbilisi Mathematical Journal

Some small orbifolds over polytopes

Soumen Sarkar

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We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We compute the cohomology rings of these orbifolds when the dimension of the orbifold is even. These orbifolds are intimately related to the notion of small cover.


The author would like to thank his advisor Mainak Poddar for helpful suggestions and stimulating discussions. The author is thankful to the anonymous referee for helpful suggestions. He would also like to thank I. S. I. for supporting his research grant during the preparation of the work was done.

Article information

Tbilisi Math. J., Volume 4 (2011), 1-27.

Received: 8 December 2010
Revised: 6 April 2011
Accepted: 13 April 2011
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55NN10
Secondary: 55N33: Intersection homology and cohomology

Orbifold group action orbifold fundamental group homology group


Sarkar, Soumen. Some small orbifolds over polytopes. Tbilisi Math. J. 4 (2011), 1--27. https://projecteuclid.org/euclid.tbilisi/1528768864

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