No description available.

This essay examines the question whether the classical theory of electrodynamics can be extended to a spacetime which locally changes dimension and if such an endeavour is mathematically possible. Recent research has developed a new generalisation of smooth manifolds, the so called M-polyfolds, which constitutes a sufficient foundation to make this endeavour a physical plausibility. These M-polyfolds then facilitate the capability to define the velocity of a curve going through a dimensionally shifting spacetime. Moreover, necessary extensions to the theory of M-polyfolds is developed in order to tailor the theory to a more physically focused framework. Concluding the essay, Maxwell’s equations on M-polyfolds are defined. / Den här uppsatsen betraktar huruvida klassisk elektrodynamik kan generaliseras till en rumtid som lokalt byter dimension samt om detta är matematiskt möjligt. Nyligen har forskningen utvecklat en generalisering av släta mångfalder, så kallade M-polyfolds, vilka ger oss en tillräcklig grund för att göra detta till en fysikalisk möjlighet. Dessa M-polyfolds möjliggör förmågan att definiera hastigheten av en kurva som går igenom en dimensionellt varierande rumtid. Därutöver utvecklas vissa nödvändiga förlängningar av teorin om M-polyfolds, detta för att skräddarsy teorin till ett mer fysikaliskt ramverk. Därefefter avslutas uppsatsen genom att definiera Maxwells ekvationer på M-polyfolds.

by Cheung Ka Luen. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 99-103.

Kam-chan Lo. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 11.

Thesis (Ed.M.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / 2031-01-01

Ho Pak Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 63-64). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- The Theorem Of Efimov --- p.6 / Chapter 2.1 --- Main Theorem --- p.6 / Chapter 2.2 --- Proof of Lemma 2.1.1 --- p.9 / Chapter 2.3 --- Proof of Lemma 2.1.2 --- p.14 / Chapter 2.4 --- Proof of Efimov's Main Lemma --- p.21 / Chapter 3 --- Hilbert's Theorem --- p.58 / Chapter 3.1 --- Hilbert's Theorem for a surface at least C2 immersed in R2 --- p.58 / Bibliography --- p.63

This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.

No description available.

For an aspherical symplectic manifold M, closed or with convex contact boundary, and with vanishing first Chern class, a Floer chain complex is defined for Hamiltonians linear at infinity with coefficients in the group ring of the fundamental group of M. For two non-degenerate Hamiltonians of the same slope continuation maps are shown to be simple homotopy equivalences. As a corollary the number of contractible Hamiltonian orbits of period 1 can be bounded from below.

Bibliography: leaves 211-217.