000			01657nam a22002057a 4500
003			OSt
005			20240830114850.0
008			190302b ||||| |||| 00| 0 eng d
020			_a9783540061052
040			_cEducational Supplies _aICTS-TIFR
050			_aQA3
100			_aBousfield, A. K.
245			_aHomotopy limits, completions and localizations
260			_aUSA: _bSpringer, _c[c1987]
300			_a348 p
505			_aI Completions and localizations 1. The R-completion of a space 2. Fibre lemmas 3. Tower lemmas 4. An R-completion of groups and its relation to the R-completion of spaces 5. R-localizations of nilpotent spaces 6. p-completions of nilpotent spaces 7. A glimpse at the R-completion of non-nilpotent spaces II Towers of fibrations, cosimplicial spaces and homotopy limits 8. Simplicial sets and topological spaces 9. Towers of fibrations 10. Cosimplicial spaces 11. Homotopy inverse limits 12. Homotopy direct limits
520			_aThe main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X. For R=Zp and X subject to usual finiteness condition, the R-completion coincides up to homotopy, with the p-profinite completion of Quillen and Sullivan; for R a subring of the rationals, the R-completion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves.
700			_aKan, D. M.
942			_2lcc _cBK
999			_c2433 _d2433