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On the Derived Functors of Destabilization and of Iterated Loop Functors

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Algebraic Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2194))

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Abstract

These notes explain how to construct small functorial chain complexes which calculate the derived functors of destabilization (respectively iterated loop functors) in the theory of modules over the mod 2 Steenrod algebra; this shows how to unify results of Singer and of Lannes and Zarati.

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Notes

  1. 1.

    This material was not presented in the original lectures.

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Acknowledgements

The author is grateful to the anonymous referee for their careful reading of the manuscript and for their suggestions.

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Authors and Affiliations

  1. Laboratoire angevin de recherches en mathématiques (LAREMA), CNRS, Université d’Angers, Université Bretagne Loire, 2 Bd lavoisier, 49045, Angers Cedex 01, France

    Geoffrey Powell

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Correspondence to Geoffrey Powell .

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Editors and Affiliations

  1. Department of Mathematics, Vietnam National University, Hanoi, Vietnam

    H.V. Hưng Nguyễn

  2. LAGA, UMR 7539 CNRS Institut Galilée, Université Paris 13, Villetaneuse, France

    Lionel Schwartz

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Powell, G. (2017). On the Derived Functors of Destabilization and of Iterated Loop Functors. In: Nguyễn, H., Schwartz, L. (eds) Algebraic Topology. Lecture Notes in Mathematics, vol 2194. Springer, Cham. https://doi.org/10.1007/978-3-319-69434-4_2

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