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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 210–226
(Mi tm3349)
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Bounded homotopy theory and the $K$-theory of weighted complexes
J. Fowler, C. Ogle Department of Mathematics, The Ohio State University, Columbus, OH, USA
Abstract:
Given a bounding class $\mathcal B$, we construct a bounded refinement $\mathcal BK(-)$ of Quillen's $K$-theory functor from rings to spaces. As defined, $\mathcal BK(-)$ is a functor from weighted rings to spaces, and is equipped with a comparison map $\mathcal BK\to K$ induced by “forgetting control”. In contrast to the situation with $\mathcal B$-bounded cohomology, there is a functorial splitting $\mathcal BK(-)\simeq K(-)\times\mathcal BK^\mathrm{rel}(-)$ where $\mathcal BK^\mathrm{rel}(-)$ is the homotopy fiber of the comparison map.
Received in March 2011
Citation:
J. Fowler, C. Ogle, “Bounded homotopy theory and the $K$-theory of weighted complexes”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 210–226; Proc. Steklov Inst. Math., 275 (2011), 199–215
Linking options:
https://www.mathnet.ru/eng/tm3349 https://www.mathnet.ru/eng/tm/v275/p210
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Abstract page: | 129 | Full-text PDF : | 46 | References: | 39 |
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