Title: The triple loop space approach to the telescope conjecture
Authors: Mark Mahowald, Doug Ravenel, Paul Shick
Addresses: Northwestern University, University of Rochester, John Carroll
University
email: mark@math.mwu.edu, drav@harpo.cc.rochester.edu, shick@jcu.edu
AMS Classification: 55
Abstract: The purpose of this paper is to describe an unsuccessful
attempt to prove that the telescope conjecture is false for all
$n \ge 2$ and all primes $p$. At the time it was originally proposed
over 20 years ago, the telescope conjecture appeared to be the simplest
and most plausible statement about the relationship between two
different localization functors. We hope that the present paper will
show that this is no longer the case. We will set up a spectral sequence
converging to the homotopy of one of the two localizations (the
geometrically defined telescope) of a certain spectrum, and it will be
apparent that only a bizarre pattern of differentials would lead to the
known homotopy of the localization defined in terms of $BP$-theory.
While we cannot exclude such a pattern, it is certainly not favored by
Occam's razor.