Geodesic
On a problem of P. S. Aleksandrov
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 539-545 
A. N. Dranishnikov. On a problem of P. S. Aleksandrov. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 539-545. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a17/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An old problem of P. S. Aleksandrov, known today as the CE-problem, is solved. Using $K$-theory, an infinite-dimensional compactum with integer cohomological dimension equal to three is constructed. This shows that cell-like maps may raise dimension. Bibliography: 9 titles.

[1] Alexandroff P., “Dimensiontheorie, ein Beitrag zur Geometrie der abgeschossenen mengen”, Math. Ann., 106 (1932), 161–238 | DOI | MR | Zbl

[2] Aleksandrov P. S., “Einige Problemstellungen in der mengentheoretischen Topologie”, Matem. sb., 1(43) (1936), 619–634 | Zbl

[3] Aleksandrov P. S., Vvedenie v gomologicheskuyu teoriyu razmernosti, Nauka, M., 1975 | MR

[4] Dranishnikov A. N, Schepin E. V., “Kletochnopodobnye otobrazheniya. Problema povysheniya razmernosti”, UMN, 41:6 (1986), 49–90 | MR | Zbl

[5] Walsh J. J., “Dimension, cohomological dimension, and cell-like mappings”, Lect. Notes in Math., 870 (1981), 105–118 | DOI | MR | Zbl

[6] Kuzminov V. I., “Gomologicheskaya teoriya razmernosti”, UMN, 23:5 (1968), 3–49 | MR

[7] Svittser R. M., Algebraicheskaya topologiya – gomotopii i gomologii, Nauka, M., 1985 | MR

[8] Bukhshtaber V. M., Mischenko A. S., “$K$-teoriya na kategorii beskonechnykh kletochnykh kompleksov”, Izv. AN SSSR. Ser. matem., 32 (1968), 560–604

[9] Spener E., Algebraicheskaya topologiya, Mir, M., 1971 | MR