Part of the NATO Science Series book series (NAII, volume 131)
The aim of this paper is to describe the concept of localization, as it usually comes up in topology, and give some examples of it. Many of the results we will describe are due to Bousfield.
KeywordsChain Complex Good Localization Homotopy Group Loop Space Homotopy Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- L. Alonso Tarrío, A. Jeremias López, and J. Lipman, Studies in duality on Noetherian formal schemes and non-Noetherian ordinary schemes, Contemporary Mathematics, vol. 244, American Mathematical Society, Providence, RI, 1999.Google Scholar
- A. K. Bousfield, The simplicial homotopy theory of iterated loop spaces, unpublished.Google Scholar
- A. K. Bousfield-, The localization of spaces with respect to homology, Topology 14 (1975), 133–150.Google Scholar
- A. K. Bousfield ——, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77), no. 2, 207–220.Google Scholar
- A. K. Bousfield ——, The localization of spectra with respect to homology, Topology 18 (1979), no. 4, 257–281.Google Scholar
- A. K. Bousfield ——, K-localizations and K-equivalences of infinite loop spaces, Proc. London Math. Soc. (3) 44 (1982), no. 2, 291–311.Google Scholar
- A. K. Bousfield ——, Localization and periodicity in unstable homotopy theory, J. Amer. Math. Soc. 7 (1994), no. 4, 831–873.Google Scholar
- _A. K. Bousfield ——, Homotopical localizations of spaces, Amer. J. Math. 119 (1997), no. 6, 1321–1354.Google Scholar
- A. K. Bousfield ——, The K-theory localizations and v1-periodic homotopy groups of H-spaces, Topology 38 (1999), no. 6, 1239–1264.Google Scholar
- A. K. Bousfield ——, On K(n)-equivalences of spaces, Homotopy invariant algebraic structures (Baltimore, MD, 1998), Contemp. Math., vol. 239, Amer. Math. Soc., Providence, RI, 1999, pp. 85–89.Google Scholar
- A. K. Bousfield ——, On the telescopic homotopy theory of spaces, Trans. Amer. Math. Soc. 353 (2001), no. 6, 2391–2426 (electronic).Google Scholar
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Springer-Verlag, Berlin, 1972, Lecture Notes in Mathematics, Vol. 304.Google Scholar
- C. Casacuberta, D. Scevenels, and J. H. Smith, Implications of large-cardinal principles in homotopical localization, preprint.Google Scholar
- E. Dror Farjoun, Homotopy and homology of diagrams of spaces, Algebraic topology (Seattle, Wash., 1985), Lecture Notes in Math., vol. 1286, Springer, Berlin, 1987, pp. 93–134.Google Scholar
- E. Dror-Farjoun, Cellular spaces, null spaces and homotopy localization, Lecture Notes in Mathematics, vol. 1622, Springer-Verlag, Berlin, 1996.Google Scholar
- D. Dugger, S. Hollander, and D. C. Isaksen, Hypercovers and simplicial presheaves, preprint (2002) http://www.math.uiuc.edu/K-theory/0563/spre.dvi/K-theory/0563/spre.dvi.
- P. Goerss, H.-W. Henn, and M. Mahowald, The homotopy of L 2 V(1) for the prime 3, preprint (2002).Google Scholar
- T. G. Goodwillie, Calculus III, preprint (2002).Google Scholar
- T. G. Goodwillie ——, Calculus. II. Analytic functors, K-Theory 5 (1991/92), no. 4, 295–332.Google Scholar
- P. S. Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs, vol. 99, American Mathematical Society, Providence, RI, 2003.Google Scholar
- N. J. Kuhn, Morava K-theories and infinite loop spaces, Algebraic topology (Arcata, CA, 1986), Lecture Notes in Math., vol. 1370, Springer, Berlin, 1989, pp. 243–257.Google Scholar
- F. Morel and V. Voevodsky, A1-homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. (1999), no. 90, 45–143 (2001).Google Scholar
- D. 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.Google Scholar
- K. Shimomura and X. Wang, The homotopy groups π* L 2(S 0) at the prime 3, preprint.Google Scholar
- C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994.Google Scholar
© Springer Science+Business Media Dordrecht 2004