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
We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a correc...We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean’s computations of the zeroth homology group.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.
基金supported by the grant of the Government of the Russian Federation for the state support of scientific research carried out under the supervision of leading scientistsagreement 14.W03.31.0030 dated 15.02.2018.1。
文摘We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean’s computations of the zeroth homology group.
