Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Prof. Dr. Wolfgang Lück
Titel: A Panorama of L2-Invariants
Abstract: We give a gentle survey about L2-invariants such as L2-Betti numbers and L2-torsion. They are modelled on their classical counterparts and defined in terms of the action of the fundamental group of the universal covering of a closed manifold using the theory of von Neumann algebras. Atiyah introduced L2-Betti numbers in connection with his L2-index theorem. Our concern will not be the technical definition or detailed proofs, but to convince the audience that L2-invariants have striking applications to problems of other areas such as algebra, analysis, geometry, group theory and topology, which on the first glance are completely unrelated. We will discuss interesting but easy to state problems and theorems in different areas and explain how they have successfully been attacked by L2-methods.
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