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This thesis treats two main topics: calibrated symplectic foliations, andlocal Lie groupoids. Calibrated symplectic foliations are one possiblegeneralization of taut foliations of 3-manifolds to higher dimensions. Theirstudy has been popular in recent years, and we collect several interestingresults. We then show how de Rham's theory of currents, and Sullivan's theoryof structure currents, can be applied in trying to understand thecalibratability of symplectic foliations. Our study of local Lie groupoidsbegins with their definition and an exploration of some of their basicproperties. Next, three main results are obtained. The first is thegeneralization of a theorem by Mal'cev. The original theorem characterizes thelocal Lie groups that are part of a (global) Lie group. We give thecorresponding result for local Lie groupoids. The second result is thegeneralization of a theorem by Olver which classifies local Lie groups in termsof Lie groups. Our generalization classifies, in terms of Lie groupoids, thoselocal Lie groupoids that have integrable algebroids. The third and final resultdemonstrates a relationship between the associativity of a local Lie groupoid,and the integrability of its algebroid. In a certain sense, the monodromygroups of a Lie algebroid manifest themselves combinatorially in a localintegration, as a lack of associativity.

Symplectic Foliations, Currents, and Local Lie Groupoids