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 non-compact spaces
and infinite groups. These new L2-invariants contain very
interesting and novel information and can be applied to problems
arising in topology, K-Theory, differential geometry,
non-commutative 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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