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

 

Pseudo-real Riemann surfaces and chiral regular maps


Authors: Emilio Bujalance, Marston D. E. Conder and Antonio F. Costa
Journal: Trans. Amer. Math. Soc. 362 (2010), 3365-3376
MSC (2000): Primary 30F10; Secondary 14H10, 57M15
Published electronically: February 24, 2010
MathSciNet review: 2601593
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Abstract: A Riemann surface is called pseudo-real if it admits anticonformal automorphisms but no anticonformal involution. In this paper, we study general properties of the automorphism groups of such surfaces and their uniformizing NEC groups. In particular, we prove that there exist pseudo-real Riemann surfaces of every possible genus $ g\geq2$. We also study pseudo-real surfaces of genus $ 2$ and $ 3$. Further, we establish a connection between pseudo-real surfaces with maximal automorphism group, and chiral $ 3$-valent regular maps, and use this to show there exist such surfaces for infinitely many genera, by exhibiting infinite families of chiral regular maps of type $ \{3,k\}$ for all $ k \ge 7$.


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Additional Information

Emilio Bujalance
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educacion a Distancia, Senda del rey, 9, 28040 Madrid, Spain
Email: eb@mat.uned.es

Marston D. E. Conder
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: m.conder@auckland.ac.nz

Antonio F. Costa
Affiliation: Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educacion a Distancia, Senda del rey, 9, 28040 Madrid, Spain
Email: acosta@mat.uned.es

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05102-0
PII: S 0002-9947(10)05102-0
Received by editor(s): June 11, 2007
Published electronically: February 24, 2010
Additional Notes: The first author was partially supported by MTM2005-01637
The second author was partially supported by N.Z. Marsden Fund UOA0721
The third author was partially supported by MTM2005-01637
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.