Controlled K-theory I: Basic theory

Details Controlled K-theory I: Basic theory Controlled K-theory I: Basic theory

2004-02-24

arxiv.org/abs/math/0402396v2

Mathematics

K-Theory and Homology

64 pages AMSTex with xypic. Revision omits material now in math.KT/0509294

Scientific paper

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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