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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Analytic Topology of Groups, Actions, Strings and Varieties
verfasst von : Alexander Reznikov
Erschienen in: Geometry and Dynamics of Groups and Spaces
Verlag: Birkhäuser Basel
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This paper is devoted to applications of Analysis to Topology. The latter is very broadly understood and includes geometric theory of finitely generated groups, group cohomology, Kazhdan groups, actions of groups on manifolds, superrigidity, fundamental groups of Kähler and quaternionic Kähler manifolds and conformal field theory. Chapters 1 and 3 treat analytical aspects of geometry of finitely generated groups. Chapter 2 uses Analysis to study groups acting on the circle. Chapter 4 studies the groups of symplectomorphisms, Chapter 5 volume-preserving actions. Chapter 6 deals with fundamental groups of Kähler and quaternionic Kähler manifolds.