Homology, Homotopy and Applications

Volume 10 (2008)

Number 3

Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson

A guide to telescopic functors

Pages: 291 – 319

DOI: https://dx.doi.org/10.4310/HHA.2008.v10.n3.a13


Nicholas J. Kuhn (Department of Mathematics, University of Virginia, Charlottesville, Va., U.S.A.)


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.

Published 1 January 2008