An Overview of Rationalization Theories of Non-simply Connected Spaces and Non-nilpotent Groups

作     者：Sergei O.IVANOV Sergei O.IVANOV

作者机构：Laboratory of Modern Algebra and ApplicationsSt.Petersburg State University14th Line29bSaint Petersburg199178Russia 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第10期

页      面：1705-1721页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Ministry of Science and Higher Education of the Russian Federation agreement 075-15-2019-1619。 

主　　题：Rationalisation localisation rational homotopy theory group theory 

摘      要：We give an overview of five rationalization theories for spaces(Bousfield-Kan’s Q-completion;Sullivan’s rationaliz ation;Bousifeld’s homology rationaliz ation;Casacuberta-Peschke’s Ω-rationalization;Gomez-Tato-Halperin-Tanré’s π-fiberwise rationalization)that extend the classical rationalization of simply connected spaces.We also give an overview of the corresponding rationalization theories for groups(Q-completion;HQ-localization;Baumslag rationalization)that extend the classical Malcev completion.