Pseudo-real Riemann surfaces and chiral regular maps
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- by Emilio Bujalance, Marston D. E. Conder and Antonio F. Costa PDF
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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 $g\geq 2$. 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 $k \ge 7$.References
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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
- MR Author ID: 43085
- Email: eb@mat.uned.es
- Marston D. E. Conder
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- MR Author ID: 50940
- ORCID: 0000-0002-0256-6978
- 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
- MR Author ID: 51935
- ORCID: 0000-0002-9905-0264
- Email: acosta@mat.uned.es
- 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 - © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 3365-3376
- MSC (2000): Primary 30F10; Secondary 14H10, 57M15
- DOI: https://doi.org/10.1090/S0002-9947-10-05102-0
- MathSciNet review: 2601593