TY  - BOOK
AU  - Bousfield,Aldridge K.
AU  - Kan,Daniel M.
ED  - SpringerLink (Online service)
TI  - Homotopy Limits, Completions and Localizations
T2  - Lecture Notes in Mathematics,
SN  - 9783540381174
AV  - QA1-939 
U1  - 510 23
PY  - 1972///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Mathematics, general
N1  - Completions and localizations -- The R-completion of a space -- Fibre lemmas -- Tower lemmas -- An R-completion of groups and its relation to the R-completion of spaces -- R-localizations of nilpotent spaces -- p-completions of nilpotent spaces -- A glimpse at the R-completion of non-nilpotent spaces -- Towers of fibrations, cosimplicial spaces and homotopy limits -- Simplicial sets and topological spaces -- Towers of fibrations -- Cosimplicial spaces -- Homotopy inverse limits -- Homotopy direct limits -- Errata -- Erratum to: The R-completion of a space -- Erratum to: Tower lemmas -- Erratum to: p-completions of nilpotent spaces
N2  - The 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
UR  - http://dx.doi.org/10.1007/978-3-540-38117-4
ER  -