## Abstract

We give a survey of a generalization of Quillen–Sullivan rational homotopy theory which gives spectral algebra models of unstable v_{n}-periodic homotopy types. In addition to describing and contextualizing our original approach, we sketch two other recent approaches which are of a more conceptual nature, due to Arone-Ching and Heuts. In the process, we also survey many relevant concepts which arise in the study of spectral algebra over operads, including topological André-Quillen cohomology, Koszul duality, and Goodwillie calculus.

Original language | English (US) |
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Title of host publication | Bousfield Classes and Ohkawa’s Theorem, BouCla 2015 |

Editors | Takeo Ohsawa, Norihiko Minami |

Publisher | Springer |

Pages | 275-323 |

Number of pages | 49 |

ISBN (Print) | 9789811515873 |

DOIs | |

State | Published - 2020 |

Event | International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 - Nagoya, Japan Duration: Aug 28 2015 → Aug 30 2015 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 309 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 |
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Country/Territory | Japan |

City | Nagoya |

Period | 8/28/15 → 8/30/15 |

## Keywords

- Bousfield–Kuhn functor
- Topological André-Quillen cohomology
- v-periodic homtopy theory

## ASJC Scopus subject areas

- General Mathematics

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