On suspensions of noncontractible compacta of trivial shape
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- by Umed H. Karimov and Dušan Repovš PDF
- Proc. Amer. Math. Soc. 127 (1999), 627-632 Request permission
Abstract:
We prove that: (i) There exists a 2-dimensional noncontractible cohomologically locally connected cell-like compactum whose reduced suspension is a contractible ANR; (ii) If the suspension $\Sigma X$ of a compactum $X$ is contractible, then $X$ is weakly contractible.References
- G. E. Bredon, Sheaf Theory, (Second Edition), Springer-Verlag, New York, 1997.
- J. H. Case and R. E. Chamberlin, Characterizations of tree-like continua, Pacific J. Math. 10 (1960), 73–84. MR 111000
- R. J. Daverman and J. J. Walsh, Examples of cell-like maps that are not shape equivalences, Michigan Math. J. 30 (1983), no. 1, 17–30. MR 694925, DOI 10.1307/mmj/1029002784
- D. M. Hyman, $\textrm {ANR}$ divisors and absolute neighborhood contractability, Fund. Math. 62 (1968), 61–73. MR 229197, DOI 10.4064/fm-62-1-61-73
- U. Kh. Karimov, An example of a space of trivial shape, all fine coverings of which are cyclic, Dokl. Akad. Nauk SSSR 286 (1986), no. 3, 531–534 (Russian). MR 834687
- R. C. Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969), 717–731. MR 251714
- Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. MR 0577064
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
- Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973
- Jan van Mill and George M. Reed (eds.), Open problems in topology, North-Holland Publishing Co., Amsterdam, 1990. MR 1078636
- C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744
- Herbert Seifert and William Threlfall, Seifert and Threlfall: a textbook of topology, Pure and Applied Mathematics, vol. 89, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. Translated from the German edition of 1934 by Michael A. Goldman; With a preface by Joan S. Birman; With “Topology of $3$-dimensional fibered spaces” by Seifert; Translated from the German by Wolfgang Heil. MR 575168
- Larry Siebenmann, Chapman’s classification of shapes: a proof using collapsing, Manuscripta Math. 16 (1975), no. 4, 373–384. MR 431183, DOI 10.1007/BF01323466
Additional Information
- Umed H. Karimov
- Affiliation: Institute of Mathematics, Tajik Academy of Sciences, Ul. Ainy 299, 734063 Dushanbe, Tajikistan
- Email: umed@td.silk.org
- Dušan Repovš
- Affiliation: Institute for Mathematics, Physics and Mechanics, University of Ljubljana, P. O. Box 2964, 1001 Ljubljana, Slovenia
- MR Author ID: 147135
- ORCID: 0000-0002-6643-1271
- Email: dusan.repovs@fmf.uni-lj.si
- Received by editor(s): June 17, 1996
- Received by editor(s) in revised form: May 29, 1997
- Communicated by: Ronald A. Fintushel
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 627-632
- MSC (1991): Primary 54C56, 55N05; Secondary 54D05, 55P40
- DOI: https://doi.org/10.1090/S0002-9939-99-04925-4
- MathSciNet review: 1610792
Dedicated: Dedicated to the memory of the Teacher Hilol Karimov