Bounded homotopy theory and the $K$-theory of weighted complexes

J. Fowler; C. Ogle

Bounded homotopy theory and the $K$-theory of weighted complexes

K-Theory and Homology 2012-04-19 v2

Authors: J. Fowler , C. Ogle

Abstract

Given a bounding class $B$ , we construct a bounded refinement $BK(-)$ of Quillen's $K$ -theory functor from rings to spaces. $BK(-)$ is a functor from weighted rings to spaces, and is equipped with a comparison map $BK \to K$ induced by "forgetting control". In contrast to the situation with $B$ -bounded cohomology, there is a functorial splitting $BK(-) \simeq K(-) \times BK^{rel}(-)$ where $BK^{rel}(-)$ is the homotopy fiber of the comparison map.

Keywords

bounded homotopy theory K-theory weighted complexes Quillen K-theory functor homotopy fiber

Cite

@article{arxiv.1102.0497,
  title  = {Bounded homotopy theory and the $K$-theory of weighted complexes},
  author = {J. Fowler and C. Ogle},
  journal= {arXiv preprint arXiv:1102.0497},
  year   = {2012}
}

Comments

25 pages, 13 diagrams; comments welcome

Bounded homotopy theory and the $K$-theory of weighted complexes

Abstract

Keywords

Cite

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