TY - GEN
T1 - Spectral algebra models of unstable vn-Periodic Homotopy Theory
AU - Behrens, Mark
AU - Rezk, Charles
N1 - Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2020.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Bousfield–Kuhn functor
KW - Topological André-Quillen cohomology
KW - v-periodic homtopy theory
UR - http://www.scopus.com/inward/record.url?scp=85077604430&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85077604430&partnerID=8YFLogxK
U2 - 10.1007/978-981-15-1588-0_10
DO - 10.1007/978-981-15-1588-0_10
M3 - Conference contribution
AN - SCOPUS:85077604430
SN - 9789811515873
T3 - Springer Proceedings in Mathematics and Statistics
SP - 275
EP - 323
BT - Bousfield Classes and Ohkawa’s Theorem, BouCla 2015
A2 - Ohsawa, Takeo
A2 - Minami, Norihiko
PB - Springer
T2 - International Conference on Bousfield Classes form a set: in Memory of Testusuke Ohkawa, BouCla 2015
Y2 - 28 August 2015 through 30 August 2015
ER -