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-Ha...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.展开更多
基金Supported by the Ministry of Science and Higher Education of the Russian Federation,agreement 075-15-2019-1619。
文摘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.
