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A nonconnective delooping of algebraic K-theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1126)

Abstract

Given a ring R, it is known that the topological space BGl(R)+ is an infinite loop space. One way to construct an infinite loop structure is to consider the category F of free R-modules, or rather its classifying space BF, as food for suitable infinite loop space machines. These machines produce connective spectra whose zeroth space is (BF)+ = ZXBG1(R)+. In this paper we consider categories C o(F) = F, C 1(F),... of parametrized free modules and bounded homomorphisms and show that the spaces (BC o)+ = (BF)+, (BC 1)+,... are the connected components of a nonconnective ω-spectrum BC(F) with π iBC(F) = Ki(R) even for negative i.

Keywords

  • Short Exact Sequence
  • Natural Transformation
  • Natural Isomorphism
  • Additive Category
  • Abelian Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Partially supported by an NSF/grant

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© 1985 Springer-Verlag

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Pedersen, E.K., Weibel, C.A. (1985). A nonconnective delooping of algebraic K-theory. In: Ranicki, A., Levitt, N., Quinn, F. (eds) Algebraic and Geometric Topology. Lecture Notes in Mathematics, vol 1126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074443

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  • DOI: https://doi.org/10.1007/BFb0074443

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15235-4

  • Online ISBN: 978-3-540-39413-6

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