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Abstract: We give a survey of the approaches to classifying foliations, starting withthe Haefliger classifying spaces and the various results and examples about thesecondary classes of foliations. Various dynamical properties of foliations areintroduced and discussed, including expansion rate, local entropy, and orbitgrowth rates. This leads to a decomposition of the foliated space into Borel ormeasurable components with these various dynamical types. The dynamicalstructure is compared with the classification via secondary classes.

Author: Steven Hurder


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