Localization and periodicity in unstable homotopy theory
HTML articles powered by AMS MathViewer
- by A. K. Bousfield
- J. Amer. Math. Soc. 7 (1994), 831-873
- DOI: https://doi.org/10.1090/S0894-0347-1994-1257059-7
- PDF | Request permission
References
- A. K. Bousfield, Types of acyclicity, J. Pure Appl. Algebra 4 (1974), 293โ298. MR 367978, DOI 10.1016/0022-4049(74)90009-7
- A. K. Bousfield, The localization of spaces with respect to homology, Topology 14 (1975), 133โ150. MR 380779, DOI 10.1016/0040-9383(75)90023-3
- A. K. Bousfield, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77), no.ย 2, 207โ220. MR 478159, DOI 10.1016/0022-4049(77)90067-6
- A. K. Bousfield, The Boolean algebra of spectra, Comment. Math. Helv. 54 (1979), no.ย 3, 368โ377. MR 543337, DOI 10.1007/BF02566281
- A. K. Bousfield, The localization of spectra with respect to homology, Topology 18 (1979), no.ย 4, 257โ281. MR 551009, DOI 10.1016/0040-9383(79)90018-1
- A. K. Bousfield, $K$-localizations and $K$-equivalences of infinite loop spaces, Proc. London Math. Soc. (3) 44 (1982), no.ย 2, 291โ311. MR 647434, DOI 10.1112/plms/s3-44.2.291 โ, The simplicial homotopy theory of iterated loop spaces (in preparation).
- A. K. Bousfield and E. M. Friedlander, Homotopy theory of $\Gamma$-spaces, spectra, and bisimplicial sets, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977) Lecture Notes in Math., vol. 658, Springer, Berlin, 1978, pp.ย 80โ130. MR 513569
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573 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.
- F. R. Cohen and J. A. Neisendorfer, Note on desuspending the Adams map, Math. Proc. Cambridge Philos. Soc. 99 (1986), no.ย 1, 59โ64. MR 809498, DOI 10.1017/S0305004100063921
- Ethan S. Devinatz, Michael J. Hopkins, and Jeffrey H. Smith, Nilpotence and stable homotopy theory. I, Ann. of Math. (2) 128 (1988), no.ย 2, 207โ241. MR 960945, DOI 10.2307/1971440
- Emmanuel Dror Farjoun, Homotopy localization and $v_1$-periodic spaces, Algebraic topology (San Feliu de Guรญxols, 1990) Lecture Notes in Math., vol. 1509, Springer, Berlin, 1992, pp.ย 104โ113. MR 1185964, DOI 10.1007/BFb0087504
- E. Dror Farjoun, The topology of $4$-manifolds, Proceedings of the Israel Mathematical Union Conference (Tel Aviv, 1987) Tel Aviv Univ., Tel Aviv, 1987, pp.ย 10โ14. MR 957946
- E. Dror Farjoun and J. H. Smith, Homotopy localization nearly preserves fibrations, Topology 34 (1995), no.ย 2, 359โ375. MR 1318881, DOI 10.1016/0040-9383(94)00025-G
- Michael J. Hopkins, Global methods in homotopy theory, Homotopy theory (Durham, 1985) London Math. Soc. Lecture Note Ser., vol. 117, Cambridge Univ. Press, Cambridge, 1987, pp.ย 73โ96. MR 932260
- Michael J. Hopkins and Jeffrey H. Smith, Nilpotence and stable homotopy theory. II, Ann. of Math. (2) 148 (1998), no.ย 1, 1โ49. MR 1652975, DOI 10.2307/120991
- Daniel M. Kan, On c. s. s. complexes, Amer. J. Math. 79 (1957), 449โ476. MR 90047, DOI 10.2307/2372558
- Lisa Langsetmo, The $K$-theory localization of loops on an odd sphere and applications, Topology 32 (1993), no.ย 3, 577โ585. MR 1231964, DOI 10.1016/0040-9383(93)90009-K
- Mark Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. (2) 116 (1982), no.ย 1, 65โ112. MR 662118, DOI 10.2307/2007048
- Mark E. Mahowald and Douglas C. Ravenel, Toward a global understanding of the homotopy groups of spheres, The Lefschetz centennial conference, Part II (Mexico City, 1984) Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1987, pp.ย 57โ74. MR 893848, DOI 10.1016/0040-9383(93)90055-z 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).
- Mark Mahowald and Robert Thompson, $K$-theory and unstable homotopy groups, Algebraic topology (Evanston, IL, 1988) Contemp. Math., vol. 96, Amer. Math. Soc., Providence, RI, 1989, pp.ย 273โ279. MR 1022687, DOI 10.1090/conm/096/1022687
- Mark Mahowald and Robert D. Thompson, The $K$-theory localization of an unstable sphere, Topology 31 (1992), no.ย 1, 133โ141. MR 1153241, DOI 10.1016/0040-9383(92)90066-Q
- Haynes Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. (2) 120 (1984), no.ย 1, 39โ87. MR 750716, DOI 10.2307/2007071
- Haynes Miller and Victor Snaith, On the $K$-theory of the Kahn-Priddy map, J. London Math. Soc. (2) 20 (1979), no.ย 2, 339โ342. MR 551463, DOI 10.1112/jlms/s2-20.2.339 โ, On ${K_ * }(Q\mathbb {R}{P^n};\;Z/2)$, CMS Conf. Proc., vol. 2, Amer. Math. Soc., Providence, RI, 1982, pp. 233-243. 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.
- G. Mislin, Localization with respect to $K$-theory, J. Pure Appl. Algebra 10 (1977/78), no.ย 2, 201โ213. MR 467732, DOI 10.1016/0022-4049(77)90023-8
- Stephen A. Mitchell, Finite complexes with $A(n)$-free cohomology, Topology 24 (1985), no.ย 2, 227โ246. MR 793186, DOI 10.1016/0040-9383(85)90057-6
- Shichirรด Oka, Existence of the unstable Adams map, Mem. Fac. Sci. Kyushu Univ. Ser. A 42 (1988), no.ย 2, 95โ108. MR 963199, DOI 10.2206/kyushumfs.42.95
- Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432
- Douglas C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106 (1984), no.ย 2, 351โ414. MR 737778, DOI 10.2307/2374308
- Douglas C. Ravenel, Progress report on the telescope conjecture, Adams Memorial Symposium on Algebraic Topology, 2 (Manchester, 1990) London Math. Soc. Lecture Note Ser., vol. 176, Cambridge Univ. Press, Cambridge, 1992, pp.ย 1โ21. MR 1232195, DOI 10.1017/CBO9780511526312.007
- Douglas C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Annals of Mathematics Studies, vol. 128, Princeton University Press, Princeton, NJ, 1992. Appendix C by Jeff Smith. MR 1192553
- Douglas C. Ravenel and W. Stephen Wilson, The Morava $K$-theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture, Amer. J. Math. 102 (1980), no.ย 4, 691โ748. MR 584466, DOI 10.2307/2374093
- Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293โ312. MR 353298, DOI 10.1016/0040-9383(74)90022-6
- E. Spanier, Infinite symmetric products, function spaces, and duality, Ann. of Math. (2) 69 (1959), 142โ198[ erratum, 733. MR 105106, DOI 10.2307/1970099
- Robert D. Thompson, A relation between $K$-theory and unstable homotopy groups with an application to $B\Sigma _p$, Algebraic topology (Oaxtepec, 1991) Contemp. Math., vol. 146, Amer. Math. Soc., Providence, RI, 1993, pp.ย 431โ439. MR 1224930, DOI 10.1090/conm/146/01238
- Zen-ichi Yosimura, Universal coefficient sequences for cohomology theories of $\textrm {CW}$-spectra, Osaka Math. J. 12 (1975), no.ย 2, 305โ323. MR 388375
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: J. Amer. Math. Soc. 7 (1994), 831-873
- MSC: Primary 55P60; Secondary 55N15, 55N20, 55Q05, 55U10
- DOI: https://doi.org/10.1090/S0894-0347-1994-1257059-7
- MathSciNet review: 1257059