The Equivariant Slice Filtration: a Primer

Details The Equivariant Slice Filtration: a Primer The Equivariant Slice Filtration: a Primer

2011-07-18

arxiv.org/abs/1107.3582v1

Mathematics

Algebraic Topology

19 pages

Scientific paper

We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the slice dimension 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.

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