Homology, Homotopy and Applications

Volume 14 (2012)

Number 2

The equivariant slice filtration: a primer

Pages: 143 – 166

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n2.a9

Author

Michael A. Hill (Department of Mathematics, University of Virginia, Charlottesville, Virginia, U.S.A.)

Abstract

We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the slice-connectivity of various families of naturally arising spectra. This leads to an analysis of pullbacks of slices defined on quotient groups, producing new collections of slices. Building on this, we determine the slice tower for the Eilenberg-Mac Lane spectrum associated to a Mackey functor for a cyclic $p$-group. We then relate the Postnikov tower to the slice tower for various spectra. Finally, we pose a few conjectures about the nature of slices and pullbacks.

Keywords

slice spectral sequence, slice filtration, equivariant homotopy

2010 Mathematics Subject Classification

55N91, 55P91, 55P92

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