Homology, Homotopy and Applications
Volume 10 (2008)
Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson
A guide to telescopic functors
Pages: 291 – 319
In the mid 1980s, Pete Bousfield and I constructed certain $p$-local “telescopic” functors $Φ_n$ from spaces to spectra, for each prime $p$, and each $n ≥ 1$. They are constructed using the full strength of the Nilpotence and Periodicity Theorems of Devanitz-Hopkins-Smith, and have some striking properties that relate the chromatic approach to homotopy theory to infinite loopspace theory.
Recently there have been a variety of new uses of these functors, suggesting that they have a central role to play in calculations of periodic phenomena. Here I offer a guide to their construction, characterization, application, and computation.
telescopic functors; periodic homotopy; unstable homotopy; stable homotopy
2010 Mathematics Subject Classification
Primary 55Q51. Secondary 55N20, 55P60, 55P65.