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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 29, Issue 2


The slice spectral sequence for the C4 analog of real K-theory

Michael A. Hill / Michael J. Hopkins / Douglas C. Ravenel
Published Online: 2016-05-27 | DOI: https://doi.org/10.1515/forum-2016-0017


We describe the slice spectral sequence of a 32-periodic C4-spectrum K[2] related to the C4 norm MU((C4))=NC2C4MU of the real cobordism spectrum MU. We will give it as a spectral sequence of Mackey functors converging to the graded Mackey functor π¯*K[2], complete with differentials and exotic extensions in the Mackey functor structure. The slice spectral sequence for the 8-periodic real K-theory spectrum K was first analyzed by Dugger. The C8 analog of K[2] is 256-periodic and detects the Kervaire invariant classes θj. A partial analysis of its slice spectral sequence led to the solution to the Kervaire invariant problem, namely the theorem that θj does not exist for j7.

Keywords: Equivariant stable homotopy theory; Kervaire invariant; Mackey functor; slice spectral sequence

MSC 2010: 55Q10; 55Q91; 55P42; 55R45; 55T99


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About the article

Received: 2016-01-22

Published Online: 2016-05-27

Published in Print: 2017-03-01

The authors were supported by DARPA Grant FA9550-07-1-0555 and NSF Grants DMS-0905160, DMS-1307896.

Citation Information: Forum Mathematicum, Volume 29, Issue 2, Pages 383–447, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2016-0017.

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