Let be the homeomorphism , .
Given an -space , denote by the –space obtained by pulling back the action on via , where is the homotopy fixed point space of the induced cyclic group action. Then .
A cyclotomic space is
equipped with a continuous circle group action
(hence a topological G-space for )
and equipped with a family of -equivariant weak homotopy equivalences , for , such that , and .
(Schl 09, def. 4.3, AGHL 12, def. 3.6)
A free loop space, , is a cyclotomic space, where acts by rotation of loops.
Let . Then is a comonad on the category of cyclotomic spaces.
The -equivariant suspension spectrum of a cyclotomic space is a cyclotomic spectrum.
Christian Schlichtkrull, The cyclotomic trace for symmetric ring spectra, Geometry & Topology Monographs 16 (2009), 545–592, (pdf), (arXiv:0903.3495)
Vigleik Angeltveit, Teena Gerhardt, Michael Hill, Ayelet Lindenstrauss, On the algebraic K-theory of truncated polynomial algebras in several variables (arXiv:1206.0247)
Last revised on June 26, 2021 at 17:03:04. See the history of this page for a list of all contributions to it.