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

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Abstract

We give an overview of five rationalization theories for spaces (Bousfield-Kan’s ℚ-completion; Sullivan’s rationalization; Bousfield’s homology rationalization; Casacuberta-Peschke’s Ω-rationalization; Gómez-Tato-Halperin-Tanré’s π1-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.

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Acknowledgements

I am grateful to Emmanuel Farjoun and Stephen Halperin for useful discussions. We also thank the referees for their time and comments.

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  1. Laboratory of Modern Algebra and Applications, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178, Russia

    Sergei O. Ivanov

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  1. Sergei O. Ivanov
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Correspondence to Sergei O. Ivanov.

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Dedicated to Professor Banghe Li on His 80th Birthday

Supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1619

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Ivanov, S.O. An Overview of Rationalization Theories of Non-simply Connected Spaces and Non-nilpotent Groups. Acta. Math. Sin.-English Ser. 38, 1705–1721 (2022). https://doi.org/10.1007/s10114-022-2063-9

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  • DOI: https://doi.org/10.1007/s10114-022-2063-9

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