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The linearisation map in algebraic K-theory

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Published/Copyright: May 12, 2006
Forum Mathematicum
From the journal Volume 18 Issue 1

Abstract

Let X be a pointed connected simplicial set with loop group G. The linearisation map in K-theory as defined by Waldhausen uses G-equivariant spaces. This paper gives an alternative description using presheaves of sets and abelian groups on the simplex category of X. In other words, the linearisation map is defined in terms of X only, avoiding the use of the less geometric loop group. The paper also includes a comparison of categorical finiteness with the more geometric notion of finite CW objects in cofibrantly generated model categories. The application to the linearisation map employs a model structure on the category of abelian group objects of retractive spaces over X.

(Communicated by Andrew Ranicki)

Received: 2004-04-07
Accepted: 2004-08-16
Published Online: 2006-05-12
Published in Print: 2006-01-26

© Walter de Gruyter

Articles in the same Issue

  1. Linear independence of L-functions
  2. Infinite interacting diffusion particles I: Equilibrium process and its scaling limit
  3. Every smooth p-adic Lie group admits a compatible analytic structure
  4. Mixed modules of finite torsion-free rank over a discrete valuation domain
  5. On generalized smooth groups
  6. E-locally cyclic abelian groups and maximal near-rings of mappings
  7. A note on Fourier coefficients of cusp forms on GLn
  8. Non-proper affine actions of the holonomy group of a punctured torus
  9. The linearisation map in algebraic K-theory
  10. The homotopy type of BG2Λ for some small matrix groups G
https://doi.org/10.1515/FORUM.2006.009

Articles in the same Issue

  1. Linear independence of L-functions
  2. Infinite interacting diffusion particles I: Equilibrium process and its scaling limit
  3. Every smooth p-adic Lie group admits a compatible analytic structure
  4. Mixed modules of finite torsion-free rank over a discrete valuation domain
  5. On generalized smooth groups
  6. E-locally cyclic abelian groups and maximal near-rings of mappings
  7. A note on Fourier coefficients of cusp forms on GLn
  8. Non-proper affine actions of the holonomy group of a punctured torus
  9. The linearisation map in algebraic K-theory
  10. The homotopy type of BG2Λ for some small matrix groups G
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