Geodesic
Topological Classification of Real Three-Dimensional Cubics
Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 886-893 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is devoted to finding topological types of nonsingular real three-dimensional cubics. It is proved that the following topological types exist: the projective space, the disjoint union of the projective space and the sphere, the projective space with handles whose number can vary from one to five. Along with these types, there is another topological type which is possibly distinct from those listed above, and this type is yet not completely described. A real cubic of this type is obtained from the projective space by replacing some solid torus in the space by another solid torus such that, under this replacement, the meridians of the first solid torus become parallels of the other solid torus, and conversely.
Keywords: three-dimensional cubic, topological type, projective space, homologically trivial curve, Harnack inequality, Betti number, sigma process.
Mots-clés : solid torus 
@article{MZM_2009_85_6_a6,
     author = {V. A. Krasnov},
     title = {Topological {Classification} of {Real} {Three-Dimensional} {Cubics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {886--893},
     year = {2009},
     volume = {85},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a6/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - Topological Classification of Real Three-Dimensional Cubics
JO  - Matematičeskie zametki
PY  - 2009
SP  - 886
EP  - 893
VL  - 85
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a6/
LA  - ru
ID  - MZM_2009_85_6_a6
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T Topological Classification of Real Three-Dimensional Cubics
%J Matematičeskie zametki
%D 2009
%P 886-893
%V 85
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a6/
%G ru
%F MZM_2009_85_6_a6
V. A. Krasnov. Topological Classification of Real Three-Dimensional Cubics. Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 886-893. http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a6/

[1] V. A. Rokhlin, “Kompleksnye topologicheskie kharakteristiki veschestvennykh algebraicheskikh krivykh”, UMN, 33:5 (1978), 77–89 | MR | Zbl

[2] V. A. Krasnov, “Zhestkaya izotopicheskaya klassifikatsiya veschestvennykh trekhmernykh kubik”, Izv. RAN. Ser. matem., 70:4 (2006), 91–134 | MR | Zbl

[3] V. A. Krasnov, “Topologicheskaya klassifikatsiya poverkhnostei Fano veschestvennykh trekhmernykh kubik”, Izv. RAN. Ser. matem., 71:5 (2007), 3–36 | MR | Zbl

[4] A. I. Degtyarev, V. I. Zvonilov, “Zhestkaya izotopicheskaya klassifikatsiya veschestvennykh algebraicheskikh krivykh bistepeni $(3,3)$ na kvadrikakh”, Matem. zametki, 66:6 (1999), 810–815 | MR | Zbl

[5] Dzh. Milnor, Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[6] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii. Monodromiya i asimptotiki integralov, Nauka, M., 1984 | MR | Zbl

[7] C. H. Clemens, P. A. Griffiths, “The intermediate Jacobian of the cubic threefold”, Ann. of Math. (2), 95:2 (1972), 281–356 | DOI | MR | Zbl

[8] Dzh. Milnor, Teoriya Morsa, Mir, M., 1965 | MR | Zbl