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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 210–226 (Mi tm3349)  

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

J. Fowler, C. Ogle

Department of Mathematics, The Ohio State University, Columbus, OH, USA
References:
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
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 199–215
DOI: https://doi.org/10.1134/S0081543811080141
Bibliographic databases:
Document Type: Article
UDC: 515.14
Language: English
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
Citation in format AMSBIB
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\by J.~Fowler, C.~Ogle
\paper Bounded homotopy theory and the $K$-theory of weighted complexes
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 210--226
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3349}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 275
\pages 199--215
\crossref{https://doi.org/10.1134/S0081543811080141}
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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