Spectral algebra models of unstable vn-Periodic Homotopy Theory

Mark Behrens, Charles Rezk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give a survey of a generalization of Quillen–Sullivan rational homotopy theory which gives spectral algebra models of unstable vn-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 languageEnglish (US)
Title of host publicationBousfield Classes and Ohkawa’s Theorem, BouCla 2015
EditorsTakeo Ohsawa, Norihiko Minami
PublisherSpringer
Pages275-323
Number of pages49
ISBN (Print)9789811515873
DOIs
StatePublished - 2020
EventInternational Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015 - Nagoya, Japan
Duration: Aug 28 2015Aug 30 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume309
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015
Country/TerritoryJapan
CityNagoya
Period8/28/158/30/15

Keywords

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

ASJC Scopus subject areas

  • General Mathematics

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