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Group actions, Teichmüller spaces and cobordisms. (English) Zbl 1373.57038

In this survey paper, the author considers hyperbolic group actions and discusses how these actions determine the global geometry and topology of the corresponding quotient spaces with conformally flat structure. The global geometry and topology of manifolds depends on different group actions of their fundamental groups. The author studies the relation between properties of the variety of discrete representations of the fundamental group of the 3-dimensional boundary of a non-trivial compact 4-dimensional cobordism with the interior having a complete hyperbolic structure and the properties of this cobordism. The paper is easy to read with helpful figures.

MSC:

57M60 Group actions on manifolds and cell complexes in low dimensions
37F30 Quasiconformal methods and Teichmüller theory, etc. (dynamical systems) (MSC2010)
57Q20 Cobordism in PL-topology
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