Homotopy Limits, Completions and Localizations

1972
ISBN: 978-3-540-06105-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 304, 352 Seiten, Format (B × H): 170 mm x 242 mm, Gewicht: 610 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kan, D. M.

Bousfield, A. K.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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.