J. References, I. Biswas, and J. Huisman, Rational real algebraic models of topological surfaces, Doc, Math, vol.12, pp.549-567, 2007.

]. J. Coste-roy87, M. Bochnak, M. Coste, and . Roy, Géométrie algébrique réelle New edition: Real algebraic geometry Algebraic approximation of mappings into spheres, Michigan Math Realization of homotopy classes by algebraic mappings The Weierstrass approximation theorem for maps between real algebraic varieties, Ergeb. Math. Grenzgeb. Ergeb. Math. Grenzgeb. J. J. Reine Angew. Math, vol.12, issue.377, pp.119-125, 1987.

]. J. Kucharz-silhol97, W. Bochnak, and R. Kucharz, Silhol, Morphisms, line bundles and moduli spaces in real algebraic geometry, Pub. Math. I.H.E.S, pp.86-91, 1997.

]. D. Chillingworth69 and . Chillingworth, A finite set of generators for the homeotopy group of a non-orientable surface, Proc. Cambridge Philos, pp.409-430, 1969.
DOI : 10.2307/1970373

]. A. Comessatti14 and . Comessatti, Sulla connessione delle superficie razionali reali, Annali di Matematica Pura ed Applicata, vol.VII, issue.2, pp.215-283, 1914.
DOI : 10.1007/BF02419577

M. Dehn, Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Fl??chen, Acta Mathematica, vol.69, issue.0, pp.135-206, 1938.
DOI : 10.1007/BF02547712

]. J. Huisman-mangolte08a, F. Huisman, and . Mangolte, The group of automorphisms of a real rational surface is n-transitive

]. J. Huisman-mangolte08b, F. Huisman, and . Mangolte, Automorphisms of real rational surfaces and weighted blow-up singularities

]. V. Iskovskikh96 and . Iskovskikh, Factorization of birational maps of rational surfaces from the viewpoint of Mori theory, Uspekhi Matematicheskikh Nauk, vol.51, issue.4, pp.3-724, 1996.
DOI : 10.4213/rm994

[. Joglar-prieto and J. Kollár, REAL ABELIAN VARIETIES WITH MANY LINE BUNDLES, Bulletin of the London Mathematical Society, vol.35, issue.01, pp.79-84, 2003.
DOI : 10.1112/S0024609302001509

]. N. Joglar-mangolte04, F. Joglar-prieto, and . Mangolte, Real algebraic morphisms and Del Pezzo surfaces of degree $2$, Journal of Algebraic Geometry, vol.13, issue.2, pp.269-285, 2004.
DOI : 10.1090/S1056-3911-03-00344-8

]. D. Johnson79 and . Johnson, Homeomorphisms of a surface which act trivially on homology, Proc. Amer, pp.75-119, 1979.
DOI : 10.1090/S0002-9939-1979-0529227-4

]. A. Kirillov57 and . Kirillov, The representations of the group of rotations of an n-dimensional Euclidean space by spherical vector fields, Dokl. Akad. Nauk SSSR (N.S.), vol.116, pp.538-541, 1957.

J. Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 1996.

]. J. Kollár-smith-corti04, K. E. Kollár, . Smith, and . Corti, Rational and nearly rational varieties, Mapping Class Groups of Nonorientable Surfaces, pp.89-109, 2002.

W. Kucharz, Algebraic morphisms into rational real algebraic surfaces, J. Algebraic Geometry, vol.8, pp.569-579, 1999.

W. B. Lickorish, On the homeomorphisms of a non-orientable surface The structure of Lie algebras of spherical vector fields and the diffeomorphism groups of S n and RP n , Sibirsk, Math. Proc. Cambridge Philos, pp.61-64, 1965.

F. Mangolte, Real algebraic morphisms on 2-dimensional conic bundles, Advances in Geometry, vol.6, issue.2, pp.199-213, 2006.
DOI : 10.1515/ADVGEOM.2006.011
URL : https://hal.archives-ouvertes.fr/hal-00000769

]. F. Ronga-vust05, T. Ronga, and . Vust, Diffeomorfismi birazionali del piano proiettivo reale, Comm. Math. Helv, vol.80, pp.517-540, 2005.

R. Silhol, Real Algebraic Surfaces, Lecture Notes in Math, vol.1392, 1989.
DOI : 10.1007/BFb0088815

K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math, vol.439, 1975.
DOI : 10.1007/BFb0070570

N. Wahl, Homological stability for the mapping class groups of non-orientable surfaces, Inventiones mathematicae, vol.136, issue.3, pp.389-424, 2008.
DOI : 10.1007/s00222-007-0085-7