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Titlebook: L2-Invariants: Theory and Applications to Geometry and K-Theory; Wolfgang Lück Book 2002 Springer-Verlag Berlin Heidelberg 2002 Algebraic

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Middle Algebraic ,-Theory and ,-Theory of von Neumann Algebras, algebra. We will explain the decomposition of a von Neumann algebra into different types. Any group von Neumann algebra is a finite von Neumann algebra. A lot of the material of the preceding chapters can be extended from group von Neumann algebras to finite von Neumann algebras as explained in Sub
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https://doi.org/10.1007/978-3-662-04687-6Algebraic K-theory; Algebraic topology; Area; K-Theory; L2-Invariants; Volume; topology
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,,-Betti Numbers,In this chapter we introduce and study ..-(co-)homology and ..-Betti numbers for Hilbert chain complexes and for regular coverings of .-complexes of finite type or of compact manifolds.
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Novikov-Shubin Invariants,In this chapter we introduce and study Novikov-Shubin invariants for Hilber chain complexes and for regular coverings of .-complexes of finite type o of compact manifolds.
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Applications to Groups,In this chapter we apply the results of Chapter 6 to questions about group theory, mainly about deficiency and Euler characteristic.
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The Singer Conjecture,This chapter is devoted to the following conjecture (see [477] and also [146, Conjecture 2]).
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