Title: A guide to telescopic functors

Author: Nicholas J. Kuhn

Email: njk4x at virginia.edu

Address: University of Virginia, Charlottesville, VA 22904

arXiv:0802.0510

Abstract:  In the mid 1980's, Pete Bousfield and I constructed certain p--local
`telescopic' functors Phi_n from spaces to spectra, for each prime p and each
positive integer n. These have striking properties that relate the chromatic
approach to homotopy theory to infinite loopspace theory: roughly put, the
spectrum Phi_n(Z) captures the v_n periodic homotopy of a space Z.

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.