Bibliography: leaves 181-190. This thesis firstly investigates K-invariant and supersymmetric actions of D-branes in curved space-time. Following this, research into charges of D-branes in a group manifold are studied. In particular, the charge groups are determined for the symmetry preserving (or untwisted) D-branes on a compact, simple, connected, simply connected group manifold. The purpose of this research is to determine these charge groups in order that they can be compared to the charge groups predicted by twisted K-theory for D-branes in a group manifold, thus providing a future important check to the theorem that D-brane charges are determined by twisted K-theory, one of the most important recent ideas in string theory.

Bibliography: leaves 181-190. / 190 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis firstly investigates K-invariant and supersymmetric actions of D-branes in curved space-time. Following this, research into charges of D-branes in a group manifold are studied. In particular, the charge groups are determined for the symmetry preserving (or untwisted) D-branes on a compact, simple, connected, simply connected group manifold. The purpose of this research is to determine these charge groups in order that they can be compared to the charge groups predicted by twisted K-theory for D-branes in a group manifold, thus providing a future important check to the theorem that D-brane charges are determined by twisted K-theory, one of the most important recent ideas in string theory. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2003

The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.

The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.

Let R be a connective ring spectrum and let M be an R-bimodule. In this paper we prove several results that relate the K-theory of R⋉M and T[superscript M, subscript R] to a “topological Witt vectors” construction W(R; M), where R ⋉ M is the square-zero extension of R by M and T [superscript M, subscript R] is the tensor algebra on M. Our main results include a desciption of the Taylor tower of K(R ⋉ (−)) and the derived functor of K̃(TR(−)) on the category of R-bimodules in terms of the Taylor tower of W(R;−). W(R;−) has an easily described Taylor tower, given explicitly by Lindenstrauss and McCarthy in [17]. Our main results serve as generalizations of the results for discrete rings in [17, 18] and also extend the computations by Hesselholt and Madsen [15] showing that π₀(TR(R; p)) is isomorphic to the p-typical Witt vectors over R when R a commutative ring. / text

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The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.

This thesis pursues the study of non-algebraic and non-Kahler compact complex manifolds by traditionally algebraic methods involving sheaves, cohomology and K-theory. To that end, Bott-Chern cohomology is developed to complement De Rham and Dolbeault cohomology. The first substantial chapter is devoted to the construction of Bott-Chern cohomology, including products. The next chapter is an investigation of Pic0(X) for non-Kahler complex manifolds. The next chapter uses line bundles represented by classes in this Pic0(X), along with Cartier divisors, to define a group of twisted cycle classes, generalizing a previous algebraic definition. On this group of twisted cycle classes, we use currents to construct a regulator map into Bott-Chern cohomology. Finally, in a chapter of conjectural statements and future directions, we explore the possibility of an alternate regulator using a cone complex of currents. We also conjecturally define a height pairing for certain kinds of compatible twisted cycle classes. / Mathematics

Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2003. / Bibliography: leaves 181-190.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [52]-53).