Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 113-119). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 236-241). Also available for download via the World Wide Web; free to University of Oregon users.

In this thesis, we develop two methods for constructing Lie groupoids. The first method is a blow-up construction, corresponding to the elementary modification of a Lie algebroid along a subalgebroid over some closed hypersurface. This construction may be specialized to the Poisson groupoids and Lie bialgebroids. We then apply this method to three cases. The first is the adjoint Lie groupoid integrating the Lie algebroid of vector fields tangent to a collection of normal crossing hypersurfaces. The second is the adjoint symplectic groupoid of a log symplectic manifold. The third is the adjoint Lie groupoid integrating the tangent algebroid of a Riemann surface twisted by a divisor. The second method is a gluing construction, whereby Lie groupoids defined on the open sets of an appropriate cover may be combined to obtain global integrations. This allows us to construct and classify the Lie groupoids integrating the given Lie algebroid. We apply this method to the aforementioned cases, albeit with small differences, and characterize the category of integrations in each case.

The theory of affine connections is, roughly speaking, a generalization of certain concepts of parallelism and differentiation defined in plane differential geometry, to the differential geometry of surfaces, and, more generally, to the geometry of differentiable manifolds. It is the purpose of this essay to relate the various stages of this generalization, and to present the essentials of the classical theory of affine connections on a differentiable manifold. [...]

In this thesis, we develop two methods for constructing Lie groupoids. The first method is a blow-up construction, corresponding to the elementary modification of a Lie algebroid along a subalgebroid over some closed hypersurface. This construction may be specialized to the Poisson groupoids and Lie bialgebroids. We then apply this method to three cases. The first is the adjoint Lie groupoid integrating the Lie algebroid of vector fields tangent to a collection of normal crossing hypersurfaces. The second is the adjoint symplectic groupoid of a log symplectic manifold. The third is the adjoint Lie groupoid integrating the tangent algebroid of a Riemann surface twisted by a divisor. The second method is a gluing construction, whereby Lie groupoids defined on the open sets of an appropriate cover may be combined to obtain global integrations. This allows us to construct and classify the Lie groupoids integrating the given Lie algebroid. We apply this method to the aforementioned cases, albeit with small differences, and characterize the category of integrations in each case.

There is no abstract available for this thesis.

There is no abstract available for this thesis.

Thesis (M.A.)--Victoria University of Wellington, 2008. / Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2010. / "Graduate Program in Computer Science." Includes bibliographical references (p. 62-64).

Thesis (Ph. D.)--University of Chicago, 1932. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Bibliography: p. 55-56.