Homotopy limits, completions and localizations
By: A.K. Bousfield, D.M. Kan.
Contributors: Kan, D. M.
Series: Lecture notes in mathematics -- 304; Lecture notes in mathematics (Berlin) -- 304.
Publisher: Springer-Verlag
Published: 1972
Place of publication: Berlin; New York
Language: eng
Number of pages: 348
Subjects: Homotopy theory.
Description: 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.