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Controlled L–theory
Andrew Ranicki and Masayuki Yamasaki
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Geometry & Topology Monographs 9
(2006) 105–153
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Abstract
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We develop an epsilon-controlled algebraic L–theory, extending our earlier work on
epsilon-controlled algebraic K–theory. The controlled L–theory is very close to
being a generalized homology theory; we study analogues of the homology
exact sequence of a pair, excision properties, and the Mayer–Vietoris exact
sequence. As an application we give a controlled L–theory proof of the classic
theorem of Novikov on the topological invariance of the rational Pontrjagin
classes.
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Keywords
controlled algebraic L–theory,
homology theory
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Mathematical Subject Classification
Primary: 57R67
Secondary: 18F25
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Publication
Received: 13 February 2004
Published: 22 April 2006
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