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The slice spectral sequence for certain \(RO({C_{p^{n}}} )\)-graded suspensions of \(H{\underline{\mathbf{Z}}}\)

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Abstract

We study the slice filtration and associated spectral sequence for a family of \(RO(C_{p^{n}})\)-graded suspensions of the Eilenberg–MacLane spectrum for the constant Mackey functor \(\underline{\mathbb Z}\). Since \(H\underline{\mathbb Z}\) is the zero slice of the sphere spectrum, this begins an analysis of how one can describe the slices of a suspension in terms of the original slices.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095, USA

    Michael A. Hill

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    M. J. Hopkins

  3. Department of Mathematics, University of Rochester, Rochester, NY, USA

    D. C. Ravenel

Authors
  1. Michael A. Hill
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  2. M. J. Hopkins
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  3. D. C. Ravenel
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Corresponding author

Correspondence to Michael A. Hill.

Additional information

This paper is dedicated to the memory of our colleague and mentor Samuel Gitler. His enthusiasm, warmth and friendship set a wonderful example and is one of the reasons it is so much fun to be an algebraic topologist. M. A. Hill was partially supported by NSF Grants DMS-0905160, DMS-1307896 and the Sloan foundation. M. J. Hopkins was partially supported the NSF Grant DMS-0906194. D. C. Ravenel was partially supported by the NSF Grants DMS-1307896 and DMS-0901560. All three authors received support from the DARPA Grants HR0011-10-1-0054-DOD35CAP and FA9550-07-1-0555.

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Hill, M.A., Hopkins, M.J. & Ravenel, D.C. The slice spectral sequence for certain \(RO({C_{p^{n}}} )\)-graded suspensions of \(H{\underline{\mathbf{Z}}}\) . Bol. Soc. Mat. Mex. 23, 289–317 (2017). https://doi.org/10.1007/s40590-016-0129-3

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  • DOI: https://doi.org/10.1007/s40590-016-0129-3

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