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

Gamboa Mutuberria, José Manuel and Bujalance, E. and 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

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Abstract

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.

Item Type:Article
Uncontrolled Keywords: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
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15250
References:

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

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