Biblioteca de la Universidad Complutense de Madrid

Automorphism Groups Of The Real Projective Plane With Holes And Their Conjugacy Classes Within Its Mapping Class Group


Gamboa, J. M. y Bujalance, E. y Cirre, F.J. (2005) Automorphism Groups Of The Real Projective Plane With Holes And Their Conjugacy Classes Within Its Mapping Class Group. Mathematische Annalen, 332 (2). pp. 253-275. ISSN 0025-5831

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 2020.


URL Oficial:


For each integer g ≥ 2 we give the complete list of groups acting as a group of dianalytic automorphisms of a real projective plane with g holes, which, in algebraic terms, correspond to birational automorphisms of real algebraic (M − 1)-curves.
We also determine those acting as the full group of automorphisms of such a surface.
Furthermore, the conjugacy classes of the finite subgroups of its mapping class group are calculated.

Tipo de documento:Artículo
Palabras clave:family of automorphism groups of compact non-orientable Klein surfaces with boundary components; real algebraic curves; ovals; finite subgroups of mapping class groups of a non-orientable surface; conjugacy classes; representatives; non-equivalent marked signatures
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:15250

Ahlfors, L.V.: The complex analytic structure of the space of closed Riemann surfaces. In: Rolf Nevanlinna et al., (ed.), Analytic functions. Princeton University Press, 1960, pp. 45–66

Alling, N.L., Greenleaf, N.: Foundations of the Theory of Klein Surfaces. Lecture Notes in Math. 219, Springer, 1971

Birman, J.S., Chillingworth, D.R.J.: On the homeotopy group of a non-orientable surface. Proc. Cambridge Phil. Soc. 71, 437–448 (1972)

Bujalance, E.: Automorphism groups of compact planar Klein surfaces. Manuscripta Math. 56, 105–124 (1986)

Bujalance, E., Bujalance, J.A., Gromadzki, G.,Mart´ınez, E.: Cyclic trigonal Klein surfaces. J. Algebra 159(2), 436–459 (1993)

Bujalance, E., Etayo, J.J., Gamboa, J.M., Gromadzki, G.: Automorphisms Groups of Compact Bordered Klein Surfaces. Lecture Notes in Math. 1439, Springer-Verlag, Berlin Heidelberg, 1990

Bujalance, E., Gamboa, J.M., Gromadzki, G.: The full automorphism groups of hyperelliptic Riemann surfaces. Manuscripta. Math. 79, 267–282 (1993)

Cirre, F.J.: Automorphism groups of real algebraic curves which are double covers of the real projective plane. Manuscripta Math. 101, 495–512 (2000)

Cirre, F.J.: On the moduli of real algebraic curves of genus 2. Pacific J. Math. 208(1), 53–72 (2003)

10. Earle, C.J.: On moduli of closed Riemann surfaces with symmetries. Ann. Math. Studies, no. 66, (Princeton, 1971), pp. 119–130

Kerckhoff, S.P.: The Nielsen realization problem. Ann. Math. 117, 235–265 (1983)

Gillete, R., Van Buskirk, J.: The word problem and consequences for the braid groups and mapping-class groups of the 2-sphere. Trans. Am. Math. Soc. 131, 277–296 (1968)

Harvey, W.J.: On branch loci in Teichm¨uller space. Trans. Am. Math. Soc. 153, 387–399 (1971)

Macbeath, A.M.: The classification of non-euclidean plane crystallographic groups. Can. J. Math. 19, 1192–1205 (1967)

Macbeath, A.M., Singerman, D.: Spaces of subgroups and Teichm¨uller space. Proc. London Math. Soc. 31(3), 211–256 (1975)

Maclachlan, C., Harvey, W.J.: On mapping class groups and Teichm¨uller spaces. Proc. London Math. Soc. 30(3), 496–512 (1975)

Natanzon, S.M.: Finite groups of homeomorphisms of a surface and real forms of complex algebraic curves. Trans. Moscow Math. Soc. 51, 1–51 (1989)

Oikawa, K.: Notes on conformal mappings of a Riemann surface onto itself. Kodai Math. Sem. Rep. 8, 23–30 (1956);A supplement to “Notes on conformal mappings of a Riemann surface onto itself”. ibid. 8, 115–116 (1956)

Teichm¨uller, O.: Extremale quasikonforme Abbildungen und quadratische Differentiale. Preuss. Akad. 22, 1940

Teichm¨uller, O.: Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl¨achen. Preuss. Akad. 4, 1943

Depositado:18 May 2012 10:07
Última Modificación:01 Mar 2016 17:36

Sólo personal del repositorio: página de control del artículo