## 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.

Original language | English (US) |
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Pages (from-to) | 3605-3614 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 8 |

DOIs | |

State | Published - 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018 American Mathematical Society.

## Keywords

- Equivariant stable homotopy theory
- Mackey functor
- Slice filtration

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