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2023

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/218296

Cohomological localizations and set-theoretical reflection

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Abstract

Homological localizations of spaces and spectra have been a fundamental tool in algebraic topology since the decade of 1970, especially in the setting of chromatic homotopy. However, it is unknown whether the existence of cohomological localizations can be proved in ZFC or not. Although this is apparently a homotopy-theoretical problem, it turned out to be closely related with set-theoretical reflection principles and therefore with the existence of large cardinals. In this note we present the state of the art with enough background so that proofs of results are readable by both topologists and set theorists.

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Teoria de l'homotopia, Topologia algebraica

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Homotopy theory, Algebraic topology

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Llibres / Capítols de llibre (Matemàtiques i Informàtica)

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CASACUBERTA, Carles. Cohomological localizations and set-theoretical reflection. Capítol del llibre: Casacuberta. Carles. Mathematics Going Forward. Vol.  Springer, num. 2023, pags. [ISBN: 978-3-031-12244-6]. ISBN 978-3-031-12244-6. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/218296

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