TY - GEN

T1 - Spectral algebra models of unstable vn-Periodic Homotopy Theory

AU - Behrens, Mark

AU - Rezk, Charles

N1 - Funding Information:
Acknowledgements The authors benefited greatly from conversations with Greg Arone, Michael Ching, Bill Dwyer, Rosona Eldred, Sam Evans, John Francis, John Harper, Gijs Heuts, Mike Hopkins, Nick Kuhn, Jacob Lurie, Mike Mandell, Akhil Mathew, Anibal Medina, Lennart Meier, Luis Alexandre Pereira, and Yifei Zhu. The authors are grateful to Norihiko Minami for encouraging this submission to these conference proceedings, honoring the memory of Tetsusuke Ohkawa. The authors would also like to thank the referee for his/her many useful comments and corrections. Both authors were supported by grants from the NSF.
Funding Information:
The authors benefited greatly from conversations with Greg Arone, Michael Ching, Bill Dwyer, Rosona Eldred, Sam Evans, John Francis, John Harper, Gijs Heuts, Mike Hopkins, Nick Kuhn, Jacob Lurie, Mike Mandell, Akhil Mathew, Anibal Medina, Lennart Meier, Luis Alexandre Pereira, and Yifei Zhu. The authors are grateful to Norihiko Minami for encouraging this submission to these conference proceedings, honoring the memory of Tetsusuke Ohkawa. The authors would also like to thank the referee for his/her many useful comments and corrections. Both authors were supported by grants from the NSF.
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 -