Title: A uniqueness theorem for stable homotopy theory
Authors: Stefan Schwede and Brooke Shipley
AMS Classification numbers: 55U35 55P42
Addresses: Stefan Schwede
Fakultat fur Mathematik
Universitat Bielefeld
33615 Bielefeld, Germany
Brooke Shipley
1395 Math. Bldg.
Purdue University
West Lafayette, IN 47907 USA
Email addresses: schwede@mathematik.uni-bielefeld.de
bshipley@math.purdue.edu
Abstract:
In this paper we study the global structure of the stable homotopy theory of
spectra. We establish criteria for when the homotopy theory associated to a
given stable model category agrees with the classical stable homotopy theory
of spectra. One sufficient condition is that the associated homotopy category
is equivalent to the stable homotopy category as a triangulated category with
an action of the ring of stable homotopy groups of spheres, $\pi^s$. In other
words, the classical stable homotopy theory, with all of its higher order
information, is determined by the homotopy category as a triangulated category
with an action of $\pi^s$. Another sufficient condition is the existence of
a small generating object (corresponding to the sphere spectrum) for which a
specific `unit map' from the infinite loop space $QS^0$ to the endomorphism
space is a weak equivalence.