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Transactions of the American Mathematical Society

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The mod $ 2$ homology of free spectral Lie algebras


Author: Omar Antolín Camarena
Journal: Trans. Amer. Math. Soc. 373 (2020), 6301-6319
MSC (2010): Primary 55P43, 55S99, 55S12
DOI: https://doi.org/10.1090/tran/8131
Published electronically: June 24, 2020
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Abstract: The Goodwillie derivatives of the identity functor on pointed spaces form an operad $ \partial _\ast (\mathrm {Id})$ in spectra. Adapting a definition of Behrens, we introduce mod $ 2$ homology operations for algebras over this operad and prove that these operations account for all the mod $ 2$ homology of free algebras on suspension spectra of simply connected spaces.


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Additional Information

Omar Antolín Camarena
Affiliation: Institute of Mathematics, UNAM, Mexico City, Mexico
Email: omar@matem.unam.mx

DOI: https://doi.org/10.1090/tran/8131
Keywords: Goodwillie calculus, homology operations
Received by editor(s): December 1, 2016
Received by editor(s) in revised form: December 31, 2019
Published electronically: June 24, 2020
Article copyright: © Copyright 2020 American Mathematical Society