Email this article Every group is the group of self-homotopy equivalences of a finite- dimensional CW-complex
- Authors: Benkhalifa M.1
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Affiliations:
- University of Sharjah
- Issue: Vol 215, No 9 (2024)
- Pages: 56-76
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/263160
- DOI: https://doi.org/10.4213/sm10038
- ID: 263160
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Abstract
Доказано, что любая группа $G$ является группой $\mathcal E(X)$ гомотопических эквивалентностей $\mathrm{CW}$-комплекса $X$ конечной размерности. Таким образом, получено обобщение известной теоремы К. Костои и А. Вируэля [9], согласно которой любая конечная группа является группой $\mathcal E(X)$ гомотопических эквивалентностей рационального эллиптического пространства $X$.Библиография: 12 названий.
References
- D. J. Anick, “Hopf algebras up to homotopy”, J. Amer. Math. Soc., 2:3 (1989), 417–453
- D. J. Anick, “An $R$-local Milnor–Moore theorem”, Adv. Math., 77:1 (1989), 116–136
- D. J. Anick, “$R$-local homotopy theory”, Homotopy theory and related topics (Kinosaki, 1988), Lecture Notes in Math., 1418, Springer-Verlag, Berlin, 1990, 78–85
- M. Benkhalifa, “Realisability of the group of self-homotopy equivalences and local homotopy theory”, Homology Homotopy Appl., 24:1 (2022), 205–215
- M. Benkhalifa, “On the group of self-homotopy equivalences of an elliptic space”, Proc. Amer. Math. Soc., 148:6 (2020), 2695–2706
- M. Benkhalifa, S. B. Smith, “The effect of cell-attachment on the group of self-equivalences of an $R$-localized space”, J. Homotopy Relat. Struct., 10:3 (2015), 549–564
- P. J. Chocano, M. A. Moron, F. Ruiz del Portal, “Topological realizations of groups in Alexandroff spaces”, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 115:1 (2021), 25, 20 pp.
- C. Costoya, D. Mendez, A. Viruel, “Realisability problem in arrow categories”, Collect. Math., 71:3 (2020), 383–405
- C. Costoya, A. Viruel, “Every finite group is the group of self-homotopy equivalences of an elliptic space”, Acta Math., 213:1 (2014), 49–62
- J. de Groot, “Groups represented by homeomorphism groups. I”, Math. Ann., 138 (1959), 80–102
- P. Hell, J. Nešetřil, Graphs and homomorphisms, Oxford Lecture Ser. Math. Appl., 28, Oxford Univ. Press, Oxford, 2004, xii+244 pp.
- D. W. Kahn, “Realization problems for the group of homotopy classes of self-equivalences”, Math. Ann., 220:1 (1976), 37–46
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