Tbilisi Mathematical Journal

Some small orbifolds over polytopes

Soumen Sarkar

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Abstract

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.

Note

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768864

Mathematical Reviews number (MathSciNet)
MR2886754

Zentralblatt MATH identifier
1278.55011

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

Keywords
Orbifold group action orbifold fundamental group homology group

Citation

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


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