A guide to telescopic functors

Abstract

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.