Homotopy idempotent functors on classifying spaces

Natàlia Castellana; Ramón Flores

Homotopy idempotent functors on classifying spaces

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2014 American Mathematical Society. Fix a prime p. Since their definition in the context of localization theory, the homotopy functors PBZ/p and CWBZ/p have shown to be powerful tools used to understand and describe the mod p structure of a space. In this paper, we study the effect of these functors on a wide class of spaces which includes classifying spaces of compact Lie groups and their homotopical analogues. Moreover, we investigate their relationship in this context with other relevant functors in the analysis of the mod p homotopy, such as Bousfield-Kan completion and Bousfield homological localization.

Original language	English
Pages (from-to)	1217-1245
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	2
Publication status	Published - 1 Jan 2015

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Cite this

Castellana, N., & Flores, R. (2015). Homotopy idempotent functors on classifying spaces. Transactions of the American Mathematical Society, 367(2), 1217-1245.

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AB - © 2014 American Mathematical Society. Fix a prime p. Since their definition in the context of localization theory, the homotopy functors PBZ/p and CWBZ/p have shown to be powerful tools used to understand and describe the mod p structure of a space. In this paper, we study the effect of these functors on a wide class of spaces which includes classifying spaces of compact Lie groups and their homotopical analogues. Moreover, we investigate their relationship in this context with other relevant functors in the analysis of the mod p homotopy, such as Bousfield-Kan completion and Bousfield homological localization.

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