Depth and Simplicity of Ohkawa’s Argument

  • Carles CasacubertaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 309)


This is an expository article about Ohkawa’s theorem stating that acyclic classes of representable homology theories form a set. We provide background in stable homotopy theory and an overview of subsequent advances in the study of Bousfield lattices. As a new result, we prove that there is a proper class of acyclic classes of nonrepresentable homology theories.


Spectra Homology theories Acyclicity Bousfield classes 



The author wishes to acknowledge the kind hospitality of the University of Nagoya during the memorial conference for Professor Ohkawa held in August 2015. The content of Sect. 7 is based on joint work of the author with Pau Casassas and Fernando Muro. The author was supported by the Agency for Management of University and Research Grants of Catalonia with references 2014 SGR 114 and 2017 SGR 585, and the Spanish Ministry of Economy and Competitiveness under AEI/FEDER research grants MTM2013-42178-P and MTM2016-76453-C2-2-P, as well as grant MDM-2014-0445 awarded to the Barcelona Graduate School of Mathematics.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Facultat de Matemàtiques i Informàtica, Universitat de Barcelona (UB)BarcelonaSpain

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