A new formulation of the equivariant slice filtration with applications to $C_p$-slices
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- by Michael A. Hill and Carolyn Yarnall PDF
- Proc. Amer. Math. Soc. 146 (2018), 3605-3614 Request permission
Abstract:
This paper provides a new way to understand the equivariant slice filtration. We give a new, readily checked condition for determining when a $G$-spectrum is slice $n$-connective. In particular, we show that a $G$-spectrum is slice greater than or equal to $n$ if and only if for all subgroups $H$, the $H$-geometric fixed points are $(n/|H|-1)$-connected. We use this to determine when smashing with a virtual representation sphere $S^V$ induces an equivalence between various slice categories. Using this, we give an explicit formula for the slices for an arbitrary $C_p$-spectrum and show how a very small number of functors determine all of the slices for $C_{p^n}$-spectra.References
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Additional Information
- Michael A. Hill
- Affiliation: Department of Mathematics, University of California Los Angeles,Los Angeles, California 90025
- MR Author ID: 822452
- ORCID: 0000-0001-8125-8107
- Email: mikehill@math.ucla.edu
- Carolyn Yarnall
- Affiliation: Department of Mathematics, California State University Dominguez Hills,Carson, California 90747
- Email: cyarnall@csudh.edu
- Received by editor(s): April 17, 2017
- Received by editor(s) in revised form: July 13, 2017
- Published electronically: May 4, 2018
- Additional Notes: The first author was supported by NSF Grant DMS-1509652.
- Communicated by: Michael A. Mandell
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3605-3614
- MSC (2010): Primary 55N91, 55P91, 55Q10
- DOI: https://doi.org/10.1090/proc/13906
- MathSciNet review: 3803684