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Controlled K-theory I: Basic theory

Frank Quinn
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Abstract

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There is a careful treatment of spectral cosheaf homology and related tools, including an ``iterated homology identity'' giving a spectrum-level version of the Leray-Serre spectral sequence.

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Frank Quinn. 2005-09-19. Controlled K-theory I: Basic theory. https://arxiv.org/abs/math/0402396

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