Residual Amenability and the Approximation of L-invariants
نویسنده
چکیده
We generalize Lück’s Theorem to show that the L-Betti numbers of a residually amenable covering space are the limit of the L-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L torsion is a homotopy invariant for such spaces. We give examples of residually amenable groups, including the Baumslag-Solitar groups.
منابع مشابه
“L-invariants of regular coverings of compact manifolds and CW -complexes”
0. Introduction 1. L-Betti numbers for CW -complexes of finite type 2. Basic conjectures 3. Low-dimensional manifolds 4. Aspherical manifolds and amenability 5. Approximating L-Betti numbers by ordinary Betti numbers 6. L-Betti numbers and groups 7. Kähler hyperbolic manifolds 8. Novikov-Shubin invariants 9. L-torsion 10. Algebraic dimension theory of finite von Neumann algebras 11. The zero-in...
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