33,175 research outputs found
Homology and Cohomology of E-infinity Ring Spectra
Every homology or cohomology theory on a category of E-infinity ring spectra
is Topological Andre-Quillen homology or cohomology with appropriate
coefficients. Analogous results hold for the category of A-infinity ring
spectra and for categories of algebras over many other operads
Stable and Unstable Operations in mod p Cohomology Theories
We consider operations between two multiplicative, complex orientable
cohomology theories. Under suitable hypotheses, we construct a map from
unstable to stable operations, left-inverse to the usual map from stable to
unstable operations. In the main example, where the target theory is one of the
Morava K-theories, this provides a simple and explicit description of a
splitting arising from the Bousfield-Kuhn functorComment: 28 pages; corrected proof of proposition 3.2, other minor
improvement
A uniqueness theorem for stable homotopy theory
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. 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 the stable homotopy groups of spheres. 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
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