Controlled L-theory

Andrew Ranicki; Masayuki Yamasaki

doi:10.2140/gtm.2006.9.105

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Controlled L-theory

Andrew Ranicki·Masayuki Yamasaki

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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.

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Andrew Ranicki, Masayuki Yamasaki. 2009-03-18. Controlled L-theory. https://doi.org/10.2140/gtm.2006.9.105

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