Gamma-Spaces and S-Algebras

  • Bjørn Ian Dundas
  • Thomas G. Goodwillie
  • Randy McCarthy
Part of the Algebra and Applications book series (AA, volume 18)


Segal’s Γ-spaces are introduced as a slight generalization of abelian groups. Though a seemingly minor generalization, this category encompasses a wide and exotic variety of new objects. In particular, the text will primarily use Γ-spaces to model spectra and strictly associative ring spectra.

The chapter begins with a gentle introduction to the algebraic properties before moving on to the homotopy theoretical properties of Γ-spaces. The chapter finishes with a discussion of how algebraic K-theory naturally leads to Γ-spaces.


Stable Equivalence Weak Equivalence Smash Product Hochschild Homology Closed Category 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Bjørn Ian Dundas
    • 1
  • Thomas G. Goodwillie
    • 2
  • Randy McCarthy
    • 3
  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Mathematics DepartmentBrown UniversityProvidenceUSA
  3. 3.Department of MathematicsUniversity of IllinoisUrbanaUSA

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