Homology of the universal covering of a co-H-space
HTML articles powered by AMS MathViewer
- by Norio Iwase, Shiroshi Saito and Toshio Sumi
- Trans. Amer. Math. Soc. 351 (1999), 4837-4846
- DOI: https://doi.org/10.1090/S0002-9947-99-02238-2
- Published electronically: May 26, 1999
- PDF | Request permission
Abstract:
The problem 10 posed by Tudor Ganea is known as the Ganea conjecture on a co-H-space, a space with co-H-structure. Many efforts are devoted to show the Ganea conjecture under additional assumptions on the given co-H-structure. In this paper, we show a homological property of co-H-spaces in a slightly general situation. As a corollary, we get the Ganea conjecture for spaces up to dimension 3.References
- Hyman Bass, Projective modules over free groups are free, J. Algebra 1 (1964), 367–373. MR 178032, DOI 10.1016/0021-8693(64)90016-X
- Israel Berstein and Emmanuel Dror, On the homotopy type of non-simply-connected co-$H$-spaces, Illinois J. Math. 20 (1976), no. 3, 528–534. MR 407837
- P. M. Cohn, Free ideal rings, J. Algebra 1 (1964), 47–69. MR 161891, DOI 10.1016/0021-8693(64)90007-9
- Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
- Karl-Heinz Strech, Über den Zusammenhang der philosphischen Kategorien Kontinuität und Diskontinuität mit den analytischen Begriffen Stetigkeit und Diskretität, Wiss. Z. Humboldt-Univ. Berlin Math.-Natur. Reihe 26 (1977), no. 1, 73–75 (German). MR 0479805
- Alexander Abian, Passages between finite and infinite, Notre Dame J. Formal Logic 19 (1978), no. 3, 452–456. MR 479800
- Tudor Ganea, Cogroups and suspensions, Invent. Math. 9 (1969/70), 185–197. MR 267582, DOI 10.1007/BF01404323
- Tudor Ganea, Some problems on numerical homotopy invariants, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, Wash., 1971) Lecture Notes in Math., Vol. 249, Springer, Berlin, 1971, pp. 23–30. MR 0339147
- Peter Hilton, Guido Mislin, and Joseph Roitberg, On co-$H$-spaces, Comment. Math. Helv. 53 (1978), no. 1, 1–14. MR 483528, DOI 10.1007/BF02566062
- Daniel M. Kan, On monoids and their dual, Bol. Soc. Mat. Mexicana (2) 3 (1958), 52–61. MR 111035
- Kazushi Komatsu, A boundary link is trivial if the Lusternik-Schnirelmann category of its complement is one, Osaka J. Math. 29 (1992), no. 2, 329–337. MR 1173992
- Nobuyuki Oda, Pairings and copairings in the category of topological spaces, Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, 83–97. MR 1147852, DOI 10.2977/prims/1195168857
- Shiroshi Saito, Notes on $\textrm {co}-H$-spaces, J. Fac. Sci. Shinshu Univ. 6 (1971), 101–106. MR 317320
- Shiroshi Saito, On higher coassociativity, Hiroshima Math. J. 6 (1976), no. 3, 589–617. MR 436128
- C. S. Seshadri, Triviality of vector bundles over the affine space $K^{2}$, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 456–458. MR 102527, DOI 10.1073/pnas.44.5.456
- George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
Bibliographic Information
- Norio Iwase
- Affiliation: Graduate School of Mathematics, Kyushu University, Ropponmatsu 4-2-1, Fukuoka 810, Japan
- Address at time of publication: Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3QY, United Kingdom
- Email: iwase@math.kyushu-u.ac.jp, n.iwase@maths.abdn.ac.uk
- Shiroshi Saito
- Affiliation: Department of Mathematics, Shinshu University, Asahi 3-1-1, Matsumoto 390, Japan
- Toshio Sumi
- Affiliation: Department of Art and Information Design, Kyushu Institute of Design, Shiobaru 4-9-1, Fukuoka 815, Japan
- Email: sumi@kyushu-id.ac.jp
- Received by editor(s): May 13, 1997
- Published electronically: May 26, 1999
- Additional Notes: The first author’s research was supported by Grant-in-Aid for Scientific Research (C)08640125 from the Ministry of Education, Science, Sports and Culture.
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 4837-4846
- MSC (1991): Primary 55P45; Secondary 19A13
- DOI: https://doi.org/10.1090/S0002-9947-99-02238-2
- MathSciNet review: 1487618