On the C*-Algebras of Foliations in the Plane

Xiaolu Wang (auth.)9780387179032, 0-387-17903-8

The main result of this original research monograph is the classification of C*-algebras of ordinary foliations of the plane in terms of a class of -trees. It reveals a close connection between some most recent developments in modern analysis and low-dimensional topology. It introduces noncommutative CW-complexes (as the global fibred products of C*-algebras), among other things, which adds a new aspect to the fast-growing field of noncommutative topology and geometry. The reader is only required to know basic functional analysis. However, some knowledge of topology and dynamical systems will be helpful. The book addresses graduate students and experts in the area of analysis, dynamical systems and topology.

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Table of contents :
Introduction….Pages 1-9
Foliations of the plane….Pages 10-34
Various trees and graphs….Pages 35-52
Distinguished trees….Pages 53-110
The C*-algebras of foliations of the plane….Pages 111-158