Volume 9 (2006)

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Controlled L–theory

Andrew Ranicki and Masayuki Yamasaki

Geometry & Topology Monographs 9 (2006) 105–153

DOI: 10.2140/gtm.2006.9.105

arXiv: math.GT/0402217

Abstract

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.

Keywords

controlled algebraic L–theory, homology theory

Mathematical Subject Classification

Primary: 57R67

Secondary: 18F25

References
Publication

Received: 13 February 2004
Published: 22 April 2006

Authors
Andrew Ranicki
School of Mathematics
University of Edinburgh
Edinburgh
EH9 3JZ
UK
Masayuki Yamasaki
Department of Applied Science
Okayama University of Science
Okayama
Okayama 700-0005
Japan