Geodesic
On a problem of P. S. Aleksandrov
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 539-545 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1989_63_2_a17,
     author = {A. N. Dranishnikov},
     title = {On a problem of {P.} {S.~Aleksandrov}},
     journal = {Sbornik. Mathematics},
     pages = {539--545},
     year = {1989},
     volume = {63},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a17/}
}
TY  - JOUR
AU  - A. N. Dranishnikov
TI  - On a problem of P. S. Aleksandrov
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 539
EP  - 545
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a17/
LA  - en
ID  - SM_1989_63_2_a17
ER  - 
%0 Journal Article
%A A. N. Dranishnikov
%T On a problem of P. S. Aleksandrov
%J Sbornik. Mathematics
%D 1989
%P 539-545
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_63_2_a17/
%G en
%F SM_1989_63_2_a17
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/

[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