Homology class of a Lagrangian Klein bottle
Izvestiya. Mathematics , Tome 73 (2009) no. 4, pp. 689-698.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that an embedded Lagrangian Klein bottle realises a non-zero mod 2 homology class in a compact symplectic four-manifold $(X,\omega)$ such that $c_1(X,\omega)\cdot[\omega] > 0$.
Keywords: Lagrangian embedding, totally real embedding, Luttinger surgery.
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S. Yu. Nemirovski. Homology class of a Lagrangian Klein bottle. Izvestiya. Mathematics , Tome 73 (2009) no. 4, pp. 689-698. http://geodesic.mathdoc.fr/item/IM2_2009_73_4_a2/

[1] C. Bailly, A. Vdovina, “Sous-espaces déterminant l'invariant de Arf et un théorème de Rohlin sur la signature”, C. R. Acad. Sci. Paris Sér. I Math., 330:3 (2000), 221–223 | DOI | MR | Zbl

[2] A. Degtyarev, I. Itenberg, V. Kharlamov, Real Enriques surfaces, Lecture Notes in Math., 1746, Springer-Verlag, Berlin, 2000 | DOI | MR | Zbl

[3] A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du côté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814 | DOI | MR | Zbl

[4] Ya. Eliashberg, L. Polterovich, “New applications of Luttinger's surgery”, Comment. Math. Helv., 69:1 (1994), 512–522 | DOI | MR | Zbl

[5] Th. Fiedler, “Totally real embeddings of the torus into $\mathbb C^2$”, Ann. Global Anal. Geom., 5:2 (1987), 117–121 | DOI | MR | Zbl

[6] A. B. Givental, “Lagrangian imbeddings of surfaces and unfolded Whitney umbrella”, Funct. Anal. Appl., 20:3 (1986), 197–203 | DOI | MR | Zbl

[7] L. Guillou, A. Marin, “Une extension d'un théorème de Rohlin sur la signature”, À la recherche de la topologie perdue, Progr. Math., 62, Birkhäuser, Boston, MA, 1986, 97–118 | MR | Zbl

[8] “Appendice: Rohlin et son théorème (d'après une lettre de O. Viro et V. Harlamov)”, À la recherche de la topologie perdue, Progr. Math., 62, Birkhäuser, Boston, MA, 1986, 153–155 | MR | MR | Zbl

[9] H.-F. Lai, “Characteristic classes of real manifolds immersed in complex manifolds”, Trans. Amer. Math. Soc., 172 (1972), 1–33 | DOI | MR | Zbl

[10] A.-K. Liu, “Some new applications of general wall crossing formula, Gompf's conjecture and its applications”, Math. Res. Lett., 3:5 (1996), 569–585 | MR | Zbl

[11] K. M. Luttinger, “Lagrangian tori in $\mathbb R^4$”, J. Differential Geom., 42:2 (1995), 220–228 | MR | Zbl

[12] D. McDuff, D. Salamon, “A survey of symplectic 4-manifolds with $b^+=1$”, Turkish J. Math., 20:1 (1996), 47–60 | MR | Zbl

[13] J. W. Milnor, D. H. Husemoller, Symmetric bilinear forms, Springer-Verlag, Berlin–Heidelberg–New York, 1973 | MR | MR | Zbl

[14] S. Yu. Nemirovski, “Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle”, Izv. Math., 66:1 (2002), 151–164 | DOI | MR | Zbl

[15] N. Yu. Netsvetaev, “An analogue of the Maslov index”, J. Math. Sci., 81:2 (1996), 2535–2537 | DOI | MR | Zbl

[16] H. Ohta, K. Ono, “Notes on symplectic 4-manifolds with $b^+_2=1$. II”, Internat. J. Math., 7:6 (1996), 755–770 | DOI | MR | Zbl

[17] L. V. Polterovich, “Strongly optical lagrangian manifolds”, Math. Notes, 45:2 (1989), 152–158 | DOI | MR | Zbl | Zbl

[18] V. Shevchishin, “Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups”, Izv. Math., 73:4 (2009), 797–859 | DOI | MR | Zbl

[19] O. Viro, “Complex orientations of real algebraic surfaces”, Topology of manifolds and varieties, Adv. Soviet Math., 18, Amer. Math. Soc., Providence, RI, 1994, 261–284 | MR | Zbl