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In algebraic topology some classical invariants such as Betti numbers and Reidemeister torsion are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to noncompact spaces and infinite groups. These new L2invariants contain very interesting and novel information and can be applied to problems arising in topology, KTheory, differential geometry, noncommutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
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