Geodesic
COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES
Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 343-347

Voir la notice de l'article provenant de la source Cambridge University Press

Let Y be a compact nonsingular real algebraic variety of positive dimension. Then one can find a compact connected nonsingular real algebraic variety X, which admits a continuous map into Y that is not homotopic to any regular map. It is hard to determine the minimum dimension of such a variety X. In this paper, new upper bounds for dim X are obtained. The main role in the constructions is played by complex algebraic cycles on Y. 
KUCHARZ, WOJCIECH. COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES. Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 343-347. doi: 10.1017/S0017089514000329
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[1] 1.Benedetti, R. and Tognoli, A., Remarks and counterexamples in the theory of real vector bundles and cycles, in Géométrie algebraique réelle et formes quadratiques, Lecture Notes in Mathematics, vol. 959 (Springer, 1982), 198–211. Google Scholar

[2] 2.Bochnak, J., Buchner, M. and Kucharz, W., Vector bundles over real algebraic varieties, K-Theory 3 (1989), 271–298. Google Scholar | DOI

[3] 3.Bochnak, J., Buchner, M. and Kucharz, W., Vector bundles over real algebraic varieties, Erratum: K-Theory 4 (1990), 103. Google Scholar

[4] 4.Bochnak, J., Coste, M. and Roy, M.-F., Real algebraic geometry, Ergeb. Math. Grenzgeb., vol. 36 (Berlin, Springer, 1998). Google Scholar

[5] 5.Bochnak, J. and Kucharz, W., On real algebraic morphisms into even-dimensional spheres Ann. Math. 128 (1988), 415–433. Google Scholar

[6] 6.Bochnak, J. and Kucharz, W., On homology classes represented by real algebraic varieties, in Singularities Symposium – Łojasiewicz 70, Banach Center Publ. 44, Inst. Math. Polish Acad. Sci. 21–35 (1998). Google Scholar

[7] 7.Bochnak, J. and Kucharz, W., Real algebraic morphisms represent few homotopy classes Math. Ann. 337 (2007), 909–921. Google Scholar | DOI

[8] 8.Borel, A. and Haefliger, A., La classe d'homologie fondamentale d'un espace analytique Bull. Soc. Math. France 89 (1961), 461–513. Google Scholar

[9] 9.Fulton, W., Intersection theory, Ergeb. Math. Grenzgeb., vol. 2 (Berlin, Springer), 1984. Google Scholar

[10] 10.Ghiloni, R., Second order homological obstructions on real algebraic manifolds Topol. Appl. 154 (2007), 3090–3094. Google Scholar

[11] 11.Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero Ann. Math. 79 (1964), 109–326. Google Scholar

[12] 12.Kollár, J., Lectures on resolutuon of singularities, Annals of Mathematics Studies, vol. 166 (Princeton University Press, Princeton, NJ, 2007). Google Scholar

[13] 13.Kucharz, W., Algebraic cycles and realification of complex projecive varieties Geom. Dedicata 54 (1995), 317–322. Google Scholar

[14] 14.Thom, R., Quelques propriétiés globales des variétés différentiables Comment. Math. Helv. 28 (1954), 17–86. Google Scholar

[15] 15.Wall, C. T. C., Determinations of the cobordism ring Ann. Math. 72 (1960), 292–311. Google Scholar

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