Controlled K-theory I: Basic Theory
Copyright policy )Controlled K-theory I: Basic Theory
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.
64 pages AMSTex with xypic. Revision omits material now in math.KT/0509294
Mathematics - Geometric Topology, Mathematics - K-Theory and Homology, FOS: Mathematics, K-Theory and Homology (math.KT), Geometric Topology (math.GT), 19D99,55N20, 57N80
Mathematics - Geometric Topology, Mathematics - K-Theory and Homology, FOS: Mathematics, K-Theory and Homology (math.KT), Geometric Topology (math.GT), 19D99,55N20, 57N80
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