Monadicity of the Bousfield-Kuhn functor
Authors:
Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier
Journal:
Proc. Amer. Math. Soc. 147 (2019), 1789-1796
MSC (2010):
Primary 55Q51
DOI:
https://doi.org/10.1090/proc/14331
Published electronically:
January 8, 2019
MathSciNet review:
3910443
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Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be the localization of the 
-category of spaces at the 
-periodic equivalences, the case 
being rational homotopy theory. We prove that 
is for 
equivalent to algebras over a certain monad on the 
-category of 
-local spectra. This monad is built from the Bousfield-Kuhn functor.
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-spaces, spectra, and bisimplicial sets, Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, Lecture Notes in Math., vol. 658, Springer, Berlin, 1978, pp. 80-130. 
-periodic homotopy groups of spheres and some compact Lie groups, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 993-1048. 
in the 
sequence, Ann. of Math. (2) 116 (1982), no. 1, 65-112. 
-periodic homotopy groups of an unstable sphere at odd primes, Trans. Amer. Math. Soc. 319 (1990), no. 2, 535-559. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 55Q51
Retrieve articles in all journals with MSC (2010): 55Q51
Additional Information
Rosona Eldred
Affiliation:
Max-Planck-Institut, Vivatsgasse 7, 53111 Bonn, Germany
Gijs Heuts
Affiliation:
Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands
Akhil Mathew
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1514
Lennart Meier
Affiliation:
Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands
DOI:
https://doi.org/10.1090/proc/14331
Received by editor(s):
March 29, 2018
Received by editor(s) in revised form:
July 10, 2018
Published electronically:
January 8, 2019
Additional Notes:
This work was begun through a Junior Trimester Program at the Hausdorff Institute of Mathematics, and we thank the HIM for its hospitality.
The second author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682922).
The third author was supported by the NSF Graduate Fellowship under grant DGE-114415 and was a Clay Research Fellow when this work was finished.
The fourth author was supported by DFG SPP 1786.
Communicated by:
Mark Behrens
Article copyright:
© Copyright 2019
American Mathematical Society
