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Localization and periodicity in unstable homotopy theory

Author(s): A. K. Bousfield
Journal: J. Amer. Math. Soc. 7 (1994), 831-873.
MSC: Primary 55P60; Secondary 55N15, 55N20, 55Q05, 55U10
MathSciNet review: 1257059
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References:

[1]
A. K. Bousfield, Types of acyclicity, J. Pure Appl. Algebra 4 (1974), 293-298. MR 0367978 (51:4220)

[2]
-, The localization of spaces with respect to homology, Topology 14 (1975), 133-150. MR 0380779 (52:1676)

[3]
-, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1977), 207-220. MR 0478159 (57:17648)

[4]
-, The Boolean algebra of spectra, Comment. Math. Helv. 54 (1979), 368-377. MR 543337 (81a:55015)

[5]
-, The localization of spectra with respect to homology, Topology 18 (1979), 257-281. MR 551009 (80m:55006)

[6]
-, $ K$-localizations and $ K$-equivalences of infinite loop spaces, Proc. London Math. Soc. 44 (1982), 291-311. MR 647434 (83g:55008)

[7]
-, The simplicial homotopy theory of iterated loop spaces (in preparation).

[8]
A. K. Bousfield and E. M. Friedlander, Homotopy theory of $ \Gamma $-spaces, spectra, and bisimplicial sets, Lecture Notes in Math., vol. 658, Springer-Verlag, Berlin and New York, 1978, pp. 80-130. MR 513569 (80e:55021)

[9]
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin and New York, 1972. MR 0365573 (51:1825)

[10]
C. Casacuberta, G. Peschke, and M. Pfenninger, On orthogonal pairs in categories and localizations, London Math. Soc. Lecture Note Ser., vol. 175, Cambridge Univ. Press, Cambridge and New York, 1992, pp. 211-223.

[11]
F. Cohen and J. Neisendorfer, A note on desuspending the Adams map, Math. Proc. Cambridge Philos. Soc. 99 (1986), 59-64. MR 809498 (87d:55015)

[12]
E. Devinatz, M. J. Hopkins, and J. H. Smith, Nilpotence and stable homotopy, Ann. of Math. (2) 128 (1988), 207-242. MR 960945 (89m:55009)

[13]
E. Dror Farjoun, The localization with respect to a map and $ {\upsilon _1}$-periodicity, Lecture Notes in Math., vol. 1509, Springer-Verlag, Berlin and New York, 1992, pp. 104-113. MR 1185964 (93k:55013)

[14]
E. Dror Farjoun, Localizations, fibrations, and conic structures (to appear). MR 957946 (89k:57035)

[15]
E. Dror Farjoun and J. H. Smith, Homotopy localization nearly preserves fibrations (to appear). MR 1318881 (96c:55014)

[16]
M. J. Hopkins, Global methods in homotopy theory, London Math. Soc. Lecture Note Ser., vol. 117, Cambridge Univ. Press, Cambridge and New York, 1987, pp. 73-96. MR 932260 (89g:55022)

[17]
M. J. Hopkins and J. H. Smith, Nilpotence and stable homotopy theory II (to appear). MR 1652975 (99h:55009)

[18]
D. M. Kan, On c.s.s. complexes, Amer. J. Math. 79 (1957), 449-476. MR 0090047 (19:759e)

[19]
L. Langsetmo, The $ K$-theory localization of loops on an odd sphere and application, Topology 32 (1993), 577-585. MR 1231964 (94e:55011)

[20]
M. Mahowald, The image of $ J$ in the EHP sequences, Ann. of Math. (2) 116 (1982), 65-112. MR 662118 (83i:55019)

[21]
M. Mahowald and D. Ravenel, Toward a global understanding of stable homotopy groups of spheres, Contemp. Math., vol. 58, part II, Amer. Math. Soc., Providence, RI, 1987, pp. 75-88. MR 893848 (88k:55011)

[22]
M. Mahowald and W. Richter, There exists a $ \upsilon _1^4$ Adams map $ M_{2\iota }^{13} \to M_{2\iota }^5$ of James filtration two (to appear).

[23]
M. Mahowald and R. Thompson, $ K$-theory and unstable homotopy groups, Contemp. Math., vol. 96, Amer. Math. Soc., Providence, RI, 1989, pp. 273-279. MR 1022687 (91d:55010)

[24]
-, The $ K$-theory localization of an unstable sphere, Topology 31 (1992), 133-141. MR 1153241 (92k:55017)

[25]
H. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. (2) 120 (1984), 39-87. MR 750716 (85i:55012)

[26]
H. Miller and V. Snaith, On the $ K$-theory of the Kahn-Priddy map, J. London Math. Soc. 20 (1979), 339-342. MR 551463 (81b:55025)

[27]
-, On $ {K_ * }(Q\mathbb{R}{P^n};\;Z/2)$, CMS Conf. Proc., vol. 2, Amer. Math. Soc., Providence, RI, 1982, pp. 233-243.

[28]
J. Milnor, On the construction FK, London Math. Soc. Lecture Note Ser., vol. 4, Cambridge Univ. Press, Cambridge and New York, 1972, pp. 119-136.

[29]
G. Mislin, Localizations with respect to $ K$-theory, J. Pure Appl. Algebra 10 (1977), 201-213. MR 0467732 (57:7585)

[30]
S. A. Mitchell, Finite complexes with $ A(n)$-free cohomology, Topology 24 (1985), 227-246. MR 793186 (86k:55007)

[31]
S. Oka, Existence of the unstable Adams map, Mem. Fac. Sci. Kyushu Univ. 42 (1988), 95-108. MR 963199 (89h:55017)

[32]
D. G. Quillen, Homotopical algebra, Lecture Notes in Math., vol. 43, Springer-Verlag, Berlin and New York, 1967. MR 0223432 (36:6480)

[33]
D. C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), 351-414. MR 737778 (85k:55009)

[34]
-, Progress report on the telescope conjecture, London Math. Soc. Lecture Note Ser., vol. 176, Cambridge Univ. Press, Cambridge and New York, 1992, pp. 1-21. MR 1232195 (94h:55023)

[35]
D. C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Stud., no. 128, Princeton Univ. Press, Princeton, NJ, 1992. MR 1192553 (94b:55015)

[36]
D. C. Ravenel and W. S. Wilson, The Morava $ K$-theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture, Amer. J. Math. 102 (1980), 691-748. MR 584466 (81i:55005)

[37]
G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. MR 0353298 (50:5782)

[38]
E. Spanier, Function spaces and duality, Ann. of Math. (2) 69 (1959), 142-198. MR 0105106 (21:3851)

[39]
R. Thompson, A relation between $ K$-theory and unstable homotopy groups with an application to $ B{\Sigma _p}$, Contemp. Math., vol. 146, Amer. Math. Soc., Providence, RI, 1993, pp. 431-439. MR 1224930 (94j:55017)

[40]
Z. Yosimura, Universal coefficient sequences for cohomology theories of CW spectra, Osaka J. Math. 12 (1975), 305-323. MR 0388375 (52:9212)

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Additional Information:

DOI: 10.1090/S0894-0347-1994-1257059-7
PII: S0894-0347-1994-1257059-7
Copyright of article: Copyright 1994, American Mathematical Society




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