Homotopy theory of Γ-spaces, spectra, and bisimplicial sets

  title={Homotopy theory of $\Gamma$-spaces, spectra, and bisimplicial sets},
  author={Aldridge Knight Bousfield and Eric Friedlander},
Algebraic Kasparov K-theory. I
This paper is to construct unstable, Morita stable and stable bivariant algebraic Kasparov K-theory spectra of k-algebras. These are shown to be homotopy invariant, excisive in each variableExpand
Iterated wreath product of the simplex category and iterated loop spaces
Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of n-fold loop spaces is shown to be equivalent to the homotopy theory of reduced Tn-spaces, where Tn is an iterated wreathExpand
Motivic symmetric spectra.
This paper demonstrates the existence of a theory of symmetric spectra for the motivic stable category. The main results together provide a categorical model for the motivic stable category which hasExpand
An equivariant van Kampen spectral sequence
Abstract This paper constructs an equivariant homotopy spectral sequence for any finite group G , any finite dimensional representation V , and two suitably connected G -CW complexes X and Y . TheExpand
The Local Structure of Algebraic K-Theory
Algebraic K-theory.- Gamma-spaces and S-algebras.- Reductions.- Topological Hochschild Homology.- The Trace K --> THH.- Topological Cyclic Homology.- The Comparison of K-theory and TC.
Definable orthogonality classes in accessible categories are small
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We proveExpand
Group completion and units in I-spaces
The category of I-spaces is the diagram category of spaces indexed by finite sets and injections. This is a symmetric monoidal category whose commutative monoids model all E-infinity spaces. WorkingExpand
The K -theory presheaf of spectra
Some applications are displayed: these include a Galois cohomological descent spectral sequence for the etale K–theory of a scheme (where the Galois group is the Grothendieck fundamental group), andExpand
Calculus of functors and model categories
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [5]. In this paper we construct various localizations of the projective modelExpand
Formal groups and stable homotopy of commutative rings
We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is closely related toExpand


Rational homotopy theory
For i ≥ 1 they are indeed groups, for i ≥ 2 even abelian groups, which carry a lot of information about the homotopy type of X. However, even for spaces which are easy to define (like spheres), theyExpand
Classifying spaces and spectral sequences
© Publications mathematiques de l’I.H.E.S., 1968, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.Expand
Homologie nicht-additiver Funktoren. Anwendungen
© Annales de l’institut Fourier, 1961, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditionsExpand