A homotopy idempotent construction by means of simplicial groups

Bastardas, Gemma; Casacuberta, Carles

doi:10.1007/bf02802510

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Homological Rationalization Of Spaces2

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2021

2022

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Cited by 3 publications

(2 citation statements)

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“…Definition. Casacuberta and Peschke developed their own theory of localization of spaces [12] (see also [25]) further developed by Bastardas and Casacuberta [2], which was initially hinted by Farjoun and Bousfield [8,Example 7.3].…”

Section: Homological Rationalization Of Spacesmentioning

confidence: 99%

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An overview of rationalization theories of non-simply connected spaces and non-nilpotent groups

Ivanov¹

2021

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We give an overview of four rationalization theories for spaces (Bousfield-Kan's Q-completion; Bousfield's homology rationalization; Casacuberta-Peschke's Ω-rationalization; Gómez-Tato-Halperin-Tanré's π 1 -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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Section: Homological Rationalization Of Spacesmentioning

confidence: 99%

“…Ω-rationalization and simplicial groups. Casacuberta and Bastardas proved that the Ω-rationalization can be defined via simplicial groups as the componentwise Baumslag rationalization [2].…”

Section: Homological Rationalization Of Spacesmentioning

confidence: 99%