Thesis (Ph.D.)--McMaster University, 2003. / Advisor: Ian Hambleton. Includes bibliographical references (leaves 109-112). Also available via World Wide Web.

The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold. / Master of Science

Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods. / Master of Science

The thesis deals with contact manifolds and their groups of transformations and relatedly with contact fibre bundles. We apply the framework of convenient calculus on in finite dimensional smooth manifolds to study the Chern-Weil theory of groups of strict contactomorphisms producing several non-vanishing type results on the cohomology of the classifying spaces of these groups. Moreover, we prove that the space of isocontact embeddings of one contact manifold to another can be given the structure of a smooth manifold and a principal bundle. Using this we describe a particular smooth model of the classifying space for the group Cont+(M; ) of (co-orientation preserving) contactomorphisms of a closed contact manifold (M; ). Lastly, we show that the standard action of the unitary group U(2) on the standard contact 3-sphere S3 induces a homotopy equivalence Cont+(S3; std) ' U(2).

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by Ng Kwok Choi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaves 39-43.

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Li Changzheng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 43-44). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.3 / Chapter 2.1 --- Clifford Algebras --- p.3 / Chapter 2.2 --- Spin Representation and Spinor Bundles --- p.7 / Chapter 2.3 --- Normed Division Algebras --- p.11 / Chapter 3 --- Associated Representations on /\. V* --- p.15 / Chapter 3.1 --- Exterior Forms and Spinors --- p.15 / Chapter 3.2 --- Direct Calculations --- p.16 / Chapter 3.3 --- "u(l,l,K) Action on V + V*" --- p.24 / Chapter 3.4 --- "su(l,l,K)´so(R1´ة0+K)" --- p.30 / Chapter 4 --- Some Applications to Geometry --- p.35 / Chapter 4.1 --- Holonomy Representations and Spinor Bundles --- p.35 / Chapter 4.2 --- The Lefschetz Action: Kahler Case --- p.37 / Chapter 4.3 --- The Lefschetz Action: HyperKahler Case --- p.41 / Bibliography --- p.43