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CO-H-spaces and localization

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Abstract

Let X be a finite simply-connected CW-complex. If for each prime p, the p-localization of X is co-H-space, then X is a co-H-space.

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References

  1. M. Arkowitz, Co-H-spaces, in Handbook of Algrebraic Topology, North-Holland, Amsterdam, 1995, pp. 1143–1173.

    Chapter  Google Scholar 

  2. M. Arkowitz and C. R. Curjel, The Hurewicz homomorphism and finite homotopy invariants, Transactions of the American Mathematical Society 110 (1964), 538–551.

    MATH  MathSciNet  Google Scholar 

  3. M. Arkowitz and G. Lupton, Rational co-H-spaces, Commentarii Mathematici Helvetici 66 (1991), no. 1, 79–108.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin, 1972.

    Book  MATH  Google Scholar 

  5. C. Costoya, Spaces in the Mislin genus of a finite, simply connected co-H 0-space, in Lusternik-Schnirelmann Category and Related Topics, Contemporary Mathematics, Vol. 316, American Mathematical Society, Providence, RI, 2002, pp. 65–72.

    Google Scholar 

  6. C. R. Curjel, A note on spaces of category ⩽ 2, Mathematische Zeitschrift 80 (1962/1963), 293–299.

    Article  MathSciNet  Google Scholar 

  7. R. H. Fox, On the Lusternik-Schnirelmann category, Annals of Mathematics (2) 42 (1941), 333–370.

    Article  Google Scholar 

  8. T. Ganea, Some problems on numerical homotopy invariants, in Symposium on Algebraic Topology, Lecture Notes in Mathematics, Vol. 249, Springer-Verlag, Berlin, 1971, pp. 23–30.

    Chapter  Google Scholar 

  9. P. Hilton, Homotopy Theory and Duality, Gordon and Breach, New York, 1963.

    Google Scholar 

  10. P. Hilton, G. Mislin and J. Roitberg, On co-H-spaces, Commentarii Mathematici Helvetici 53 (1978), no. 1, 1–14.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. R. Hubbuck and N. Iwase, A p-complete version of the Ganea conjecture for co-Hspaces, in Lusternik-Schnirelmann Category and Related Topics, Contemporary Mathematics, Vol. 316, American Mathematical Society, Providence, RI, 2002, pp. 127–133.

    Google Scholar 

  12. N. Iwase, Co-H-spaces and the Ganea conjecture, Topology 40 (2001), no. 2, 223–234.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. M. Kane, The Homology of Hopf Spaces, North-Holland Mathematical Library, Vol. 40, North-Holland, Amsterdam, 1988.

    MATH  Google Scholar 

  14. M. Mimura, G. Nishida and H. Toda, Localization of CW-complexes and its applications, Journal of the Mathematical Society of Japan 23 (1971), 593–624.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Mimura and H. Toda, On p-equivalences and p-universal spaces, Commentarii Mathematici Helvetici 46 (1971), 87–97.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Pan, Homotopy localization and H-spaces, The Bulletin of the London Mathematical Society 34 (2002), 677–680.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Roitberg, The Lusternik-Schnirelmann category of certain infinite CW-complexes, Topology 39 (2000), no. 1, 95–101.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Zabrodsky, Hopf Spaces, North Holland Publishing Co., Vol. 22, North-Holland, Amsterdam-NewYork-Oxford, 1976.

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Alxebra, Universidade de Santiago de Compostela (USC), 15782, Santiago de Compostela, Spain

    Cristina Costoya

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  1. Cristina Costoya
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Correspondence to Cristina Costoya.

Additional information

The author was partially supported by MEC (Spain), Grant MTM2006-15338-C02 (European FEDER support included) and by Xunta de Galicia, Grant PGIDITI06PXIB371128PR

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Costoya, C. CO-H-spaces and localization. Isr. J. Math. 180, 69–92 (2010). https://doi.org/10.1007/s11856-010-0094-x

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  • DOI: https://doi.org/10.1007/s11856-010-0094-x

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