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Bounded homotopy theory and the K-theory of weighted complexes

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Abstract

Given a bounding class B, we construct a bounded refinement BK(−) of Quillen’s K-theory functor from rings to spaces. As defined, BK(−) is a functor from weighted rings to spaces, and is equipped with a comparison map BK → K induced by “forgetting control.” In contrast to the situation with B-bounded cohomology, there is a functorial splitting BK(−) ≅ K(−)×BK rel(−) where BK rel(−) is the homotopy fiber of the comparison map.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210-1174, USA

    J. Fowler & C. Ogle

Authors
  1. J. Fowler
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  2. C. Ogle
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Fowler, J., Ogle, C. Bounded homotopy theory and the K-theory of weighted complexes. Proc. Steklov Inst. Math. 275, 199–215 (2011). https://doi.org/10.1134/S0081543811080141

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