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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of regular maps of negative prime Euler characteristic


Authors: Antonio Breda d'Azevedo, Roman Nedela and Jozef Sirán
Journal: Trans. Amer. Math. Soc. 357 (2005), 4175-4190
MSC (2000): Primary 05C10; Secondary 57M15, 57M60, 20F65, 05C25
Published electronically: November 4, 2004
MathSciNet review: 2159705
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Abstract: We give a classification of all regular maps on nonorientable surfaces with a negative odd prime Euler characteristic (equivalently, on nonorientable surfaces of genus $p+2$ where $p$is an odd prime). A consequence of our classification is that there are no regular maps on nonorientable surfaces of genus $p+2$where $p$ is a prime such that $p\equiv 1$ (mod $12$) and $p\ne 13$.


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Additional Information

Antonio Breda d'Azevedo
Affiliation: Departamento de Matematica, Universidade de Aveiro, Aveiro, Portugal
Email: breda@mat.ua.pt

Roman Nedela
Affiliation: Institute of Mathematics, Slovak Academy of Science, Banská Bystrica, Slovakia
Email: nedela@savbb.sk

Jozef Sirán
Affiliation: Department of Mathematics, SvF, Slovak Univ. of Technology, Bratislava, Slovakia
Email: siran@math.sk

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03622-0
PII: S 0002-9947(04)03622-0
Keywords: Regular maps, nonorientable surfaces, quotients of triangle groups, prime Euler characteristic
Received by editor(s): April 9, 2003
Received by editor(s) in revised form: December 11, 2003
Published electronically: November 4, 2004
Additional Notes: The authors thank the Department of Mathematics of the University of Aveiro and the Research Unit “Matemática e Aplicações” for supporting this project.
The second author acknowledges support from the VEGA Grant No. 2/2060/22 and from the APVT Grant No. 51-012502.
The third author was sponsored by the U.S.-Slovak Science and Technology Joint Fund under Project Number 020/2001, and also in part by the VEGA Grant No. 1/9176/02 and the APVT Grant No. 20-023302.
Article copyright: © Copyright 2004 American Mathematical Society