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1997 | 152 | 3 | 211-230
Tytuł artykułu

Connected covers and Neisendorfer's localization theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann category may be infinite, and they may serve as domains for nontrivial phantom maps.
Słowa kluczowe
Rocznik
Tom
152
Numer
3
Strony
211-230
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-24
poprawiono
1996-12--02
Twórcy
  • Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 København Ø, Denmark, moller@math.ku.dk
Bibliografia
  • [1] J. F. Adams and N. J. Kuhn, Atomic spaces and spectra, Proc. Edinburgh Math. Soc. 32 (1989), 473-481.
  • [2] A. K. Bousfield, Localization and periodicity in unstable homotopy theory, J. Amer. Math. Soc. 7 (1994), 831-873.
  • [3] A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, Berlin, 1972.
  • [4] C. Casacuberta, Recent advances in unstable localization, in: CRM Proc. Lecture Notes 6, Amer. Math. Soc., 1994, 1-22.
  • [5] F. R. Cohen, J. C. Moore and J. A. Neisendorfer, Torsion in homotopy groups, Ann. of Math. 109 (1979), 121-168.
  • [6] F. R. Cohen, J. C. Moore and J. A. Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math. 110 (1979), 549-565.
  • [7] A. Dold, Relations between ordinary and extraordinary homology, in: J. F. Adams, Algebraic Topology - A Student's Guide, London Math. Soc. Lecture Note Ser. 4, Cambridge Univ. Press, London, 1972, 167-177.
  • [8] E. Dror Farjoun, Homotopy localization and $v_1$-periodic spaces, in: Lecture Notes in Math. 1509, Springer, 1991, 104-113.
  • [9] E. Dror Farjoun, Localizations, fibrations and conic structures, preprint, Hopf Topology Archive, 1992.
  • [10] E. Dyer and J. Roitberg, Note on sequences of Mayer-Vietoris type, Proc. Amer. Math. Soc. 80 (1980), 660-662.
  • [11] B. Gray and C. A. McGibbon, Universal phantom maps, Topology 32 (1993), 371-394.
  • [12] I. M. James, Lusternik-Schnirelmann category, in: Handbook of Algebraic Topology, I. M. James (ed.), North-Holland, 1995, Chapter 27.
  • [13] M. J. Hopkins and D. C. Ravenel, Suspension spectra are harmonic, Bol. Soc. Mat. Mexicana (2) 37 (1992), 271-279.
  • [14] M. J. Hopkins, D. C. Ravenel and W. S. Wilson, Morava Hopf algebras and spaces K(n) equivalent to finite Postnikov systems, preprint, Hopf Topology Archive, 1994.
  • [15] J. Lannes et L. Schwartz, A propos de conjectures de Serre et Sullivan, Invent. Math. 83 (1986), 593-603.
  • [16] C. A. McGibbon, The Mislin genus of a space, in: CRM Proc. Lecture Notes 6, Amer. Math. Soc., 1994, 75-102.
  • [17] C. A. McGibbon, Phantom maps, in: Handbook of Algebraic Topology, I. M. James (ed.), North-Holland, 1995, Chapter 25.
  • [18] C. A. McGibbon, Infinite loop spaces and Neisendorfer localization, Proc. Amer. Math. Soc., to appear.
  • [19] C. A. McGibbon and J. M. Møller, On spaces of the same n-type for all n, Topology 31 (1992), 177-201.
  • [20] C. A. McGibbon and C. W. Wilkerson, Loop spaces of finite complexes at large primes, Proc. Amer. Math. Soc. 96 (1986), 698-702.
  • [21] H. Miller, The Sullivan fixed point conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87.
  • [22] J. M. Møller, The normalizer of the Weyl group, Math. Ann. 294 (1992), 59-80.
  • [23] J. A. Neisendorfer, Localization and connected covers of finite complexes, in: Contemp. Math. 181, Amer. Math. Soc., 1995, 385-390.
  • [24] J. A. Neisendorfer and P. S. Selick, Some examples of spaces with or without exponents, in: CMS Conf. Proc. 2, Part 1, Amer. Math. Soc., 1982, 343-357.
  • [25] D. C. Ravenel and W. S. Wilson, The Morava K-theories of Eilenberg-MacLane spaces and the Conner-Floyd conjecture, Amer. J. Math. 102 (1980), 691-748.
  • [26] D. Rector, Loop structures on the homotopy type of $S^3$, in: Lecture Notes in Math. 249, Springer, 1971, 99-105.
  • [27] J. D. Stasheff, H-spaces from a Homotopy Point of View, Lecture Notes in Math. 161, Springer, Berlin, 1970.
  • [28] D. Sullivan, The genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974), 1-79.
  • [29] C. W. Wilkerson, Classification of spaces of the same n-type for all n, Proc. Amer. Math. Soc. 60 (1976), 279-285.
  • [30] C. W. Wilkerson, Applications of minimal simplicial groups, Topology 15 (1976), 111-130.
  • [31] A. Zabrodsky, Hopf Spaces, North-Holland Math. Stud. 22, North-Holland, Amsterdam, 1976.
  • [32] A. Zabrodsky, On phantom maps and a theorem of H. Miller, Israel J. Math. 58 (1987), 129-143.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i3p211bwm
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